one embodiment of a tray 20 is shown in fig1 . the tray has a base 22 and circumscribing wall structure 24 extending from a junction 25 with perimeter of the base to an upper rim 26 . the wall structure includes two sloping , continuous and generally vertical sides ( side walls ) 28 and two generally vertical slotted ends ( end walls ) 30 . the sides 28 and ends 30 extend to upper edges formed as portions of the rim 26 . the base 22 has an underside or bottom 32 ( fig3 & amp ; 4 ) which forms a tray bottom and has an upper surface or top side 34 ( fig5 ) which may support one or more cartons 36 contained within the wall structure . the base has upwardly - open channels or grooves 38 ( fig2 ) which run from end to end , joining each end 30 at the base of a slot 40 . the grooves 38 separate and are interspersed with ridges or lands 42 . the base has upwardly - open transverse notches 44 passing from side to side along each of the ridges . the exemplary notches 44 are shallower than the grooves 38 . the exemplary wall structure 24 has an inboard face / surface 50 and an outboard face / surface 52 each with respective portions along the sides 28 and ends 30 to form inboard and outboard surfaces thereof . the exemplary trays are of substantially rectangular planform having an overall width w 1 and an overall length l 1 . additionally , the tray has an interior width w 2 and length l 2 ( measured as associated widths and lengths of the largest rectangular carton which may be supported on the upper surface of the base ). an exemplary overall / exterior tray height is shown as h 1 from the underside of the base to the upper rim 26 . an exemplary base thickness / height is h 2 , leaving an interior depth / height of h 3 equals h 1 minus h 2 . for reference , a longitudinal vertical medial plane is shown as 500 and a transverse vertical medial plane is shown as 502 . the sides and ends of the tray slope outward slightly so that when trays are stacked on each other , the space required for storage of trays is kept needed . the outboard surface 52 is stepped ( fig4 ) with an upwardly divergent angled lower portion 55 , a vertical upper portion 56 , and an intermediate wedge 57 joining the upper and lower portions . when stacked , the trays nest with the intermediate portion 57 contacting or closely facing the upper rim 26 of the wall of the tray immediately below . the slots 40 extend along / through the end walls 30 and are open to / at the upper edges of the end walls . the slots separate interspersed intact portions 60 of the end walls . the slots 40 and their associated grooves 38 are positioned and dimensioned to accommodate fingers ( discussed below ) of a detraying system for removing cartons . the exemplary slots / grooves each have a characteristic width w 3 . the slots / grooves separate intact end wall portions 60 and ridges 42 having a width w 4 . an on - center spacing s 1 of the slots / grooves is measured as half of the respective width w 3 of each two adjacent such slots / grooves plus the width w 4 of the intervening intact end portions / ridges . similarly , an on - center spacing s 2 of the intact end portions / ridges is half of the respective widths w 4 of two adjacent such end portions / ridges plus the width w 3 of the intervening slot / groove . as is discussed further below , the widths w 3 and w 4 and spacings s 1 and s 2 can vary for the different slots / grooves and intact end wall portions / ridges . in the exemplary tray , respective left and right terminal portions 64 of the intact end walls ( of associated corner portions 66 of the wall structure ) have widths w 5 which are greater than w 4 . this allows for relatively robust corner portions . this robustness may provide one or more of : lateral support of the side walls ; vertical strength for stacking ; longitudinal strength for retaining tray contents ; and surface area for bar codes / labels / other indicia . it is desirable to provide operation with multiple sizes of trays . different tray lengths may readily be accommodated . however , accommodating different tray width creates problems . the exemplary tray 20 has five grooves / slots . if a larger tray were to merely be a laterally extended version ( having more slots of the same width and spacing ), there would be problems accommodating both trays . specifically , if the detraying machine had fingers positioned to engage the slots of the larger tray , those fingers would interfere with one of the corner portions 66 of the smaller tray . accordingly , as is discussed in further detail below , the basic tray of fig1 can form one part of a system where a more complicated arrangement of detraying machine fingers are provided along with a more complicated distribution of slots in larger trays . an example is described below wherein the tray of fig1 is the smallest of three exemplary sizes ( more particularly , widths ) of tray . fig7 & amp ; 8 show an exemplary intermediate / medium size tray 20 ′ and fig9 & amp ; 10 show an exemplary large tray 20 ″ in the three - width system . as is discussed further below , each of the trays is of generally similar construction with similar relatively wide corner portions but with different groove / slot distribution . the variation in groove / slot distribution may best be visualized by first looking at the finger distribution of the detraying machine . exemplary exterior dimensions l 1 and w 1 of the tray 20 are nineteen inches ( 48 cm ) and fourteen inches ( 36 cm ) and inside dimensions l 2 and w 2 are seventeen inches and twelve inches . for t he medium tray 20 ′ these are : twenty - six inches ( 66 cm ); nineteen inches ; twenty - four inches ( 61 cm ); and seventeen inches . for the large tray 20 ″ these are : forty - one inches ( 104 cm ); twenty - six inches ; thirty - nine inches ( 99 cm ); and twenty - four inches . these interior dimensions are as measured at the interior base of the side walls . each of the three sizes has overall height h 1 of an exemplary three inches ( 8 cm ). the base height h 2 of each size tray is an exemplary 0 . 75 inch ( 2 cm ), and interior depth h 3 of an exemplary 2 . 25 inches ( 6 cm ). these different sizes are similar in form but vary from each other , in addition to overall size , in the number and distribution of slots and the corresponding grooves . as is discussed further below , each tray has mirror image symmetry across the planes 500 and 502 . thus , each tray can be processed with either end leading . the device is not limited to the use of only three sizes of trays and alternative embodiments could have more or fewer tray sizes and could use sizes different from those of the exemplary embodiment . the exemplary trays are made of plastic ( e . g ., a single - piece unitary polypropylene molding ) of sufficient strength to bear the load of the cartons but alternative embodiments could be made of different plastics , metal or other materials . fig1 shows an end view of three sizes of trays 20 , 20 ′, and 20 ″, and the relationship the slots in each size tray bear to the vertical slots of the other size trays and to fingers of a detraying machine 200 . as is discussed further below , the detraying machine forms a portion of a transfer system for transferring cartons from the trays . the fingers are positioned to pass partially through the associated tray slots and grooves to remove ( detray ) the cartons from the trays . the exemplary machine 200 has nine fingers labeled 202 a - 202 i . these nine fingers are configured for use with an exemplary four - tray system including a fourth tray ( not shown ) even wider than the tray 20 ″. the first eight fingers 202 a - 202 h , alone , facilitate use of the three - tray system . in the exemplary system 200 , the trays pass along a conveyor system with a first side 28 in a predetermined lateral registry with the system 200 ( e . g ., against a first side 204 of a conveyor carrying the trays and their cartons ). as the small tray 20 passes through the system , a first terminal group ( i . e ., starting from one side of the array of fingers ) 202 a - 202 e of an exemplary five of the fingers passes through respective slots / grooves ( for purpose of reference , the slots 40 being subreferenced 40 a - 40 e but the grooves 38 not being individually referenced ). each of the fingers is shown having a width w 10 . an on - center spacing s 10 is also shown between adjacent fingers ( and subreferenced s 10a - s 10h for the respective pairs of fingers ). a gap width between fingers is shown as w 11 . as is discussed further below , the spacing or pitch s 10 for the group of fingers 202 a - 202 e may be constant or close thereto . fig1 shows respective inter - finger gaps 210 a - 210 h . the width w 11 of the gap 210 e is substantially larger than the width of the gaps 210 a - 210 d within the first group of fingers 202 a - 202 e . this gap is effective to accommodate the second side wall and associated corners of the small tray 20 . this gap width may be more than twice the width of the gaps 210 a - 210 d . as is discussed further below , the gap 210 e may represent approximately the loss of a single finger from an array of constant spacing . however , the spacers may be further modified to improve coverage and feeding . for example , in the table below , two examples are given one with exactly constant spacing of the first five fingers and the other with a slightly increased spacing between the third and fourth and a correspondingly slightly decreased spacing between the fourth and fifth . this may improve feeding consistency when the various sizes of trays are considered . for removing cartons from the intermediate / medium tray 20 ′, the first group of fingers 202 a - 202 e are used along with the next finger 202 f . these respectively pass through slots 40 ′ a - 40 ′ e and 40 ′ g ( and their associated grooves ) of the tray 20 ′. no finger passes through the penultimate slot 40 ′ f . the slot 40 ′ f exists for side - to - side symmetry ( so that it would be in the position of slot 40 ′ b if the tray is reversed ). this symmetry allows trays to be used in either of two orientations . when passing the medium tray , its second side wall and associated corner portions pass through the gap 210 f . thus , the gap 210 f may be of similar dimension to the gap 210 e . similarly , for removing cartons from the large tray 20 ″, the first group of fingers 202 a - 202 e are also used along with the next finger 202 f and the next two fingers 202 g and 202 h . these respectively pass through slots 40 ′ a - 40 ′ e , 40 ′ g , 40 ′ i , and 40 ′ j ( and their associated grooves ) of the tray 20 ″. no finger passes through the slots 40 ′ f and 40 ′ h . these slots 40 ′ f and 40 ′ h exist , as noted above , for side - to - side symmetry ( so that they would be in the positions of slots 40 ′ e and 40 ′ c if the tray is reversed as in a mirror image across the plane 500 ). when passing the large tray , its second side wall and associated corner portions pass through the gap 210 h . thus , the gap 210 h ( if a finger 202 i is present ) may be of similar dimension to the gaps 210 e and 210 f . exemplary slot and / or groove width may be measured at a given particular height or heights or as an average ( e . g ., a mean , a median , or a mode ). this width is shown as essentially constant along the grooves and essentially constant along a lower / proximal portion of the intact wall portions ( e . g ., to about the level of the base upper surface ). thus , the intact wall portions &# 39 ; widths may similarly be measured . exemplary slots diverge upwardly / distally . accordingly , the exemplary intact wall portions converge upwardly / distally along upper / distal portions thereof . exemplary finger spacing and slot width are shown in table 1 where widths are measured along the lower / proximal portions . example 1 repeats dimensions from the drawings of the priority application . fig1 - 15 show an exemplary eight - fingered machine 200 ′ as part of a system including a tray delivery conveyor 240 and a tray content ( carton ) removal conveyor 242 . each finger is shown including an associated wedge - like tip 244 . these tips 244 are sized to be a close but non - interfering fit in the grooves in the base of the approaching tray . the bottom surface 246 of each wedge / tip is oriented such that it is generally parallel to the upper ( transport ) surface of the conveyor 240 transporting the tray and is positioned a sufficient distance above conveyor 240 for the base of the tray along the grooves to pass below the wedge . the upper surface 246 of each wedge / tip slopes at an angle acute enough that the wedge can slip between the moving tray and the bottom surface of the carton carried by the tray , and is positioned to insert into the cavity formed by the groove in the base of the tray below the carton . exemplary wedges / tips are arranged parallel to each other so that their upper surfaces combine to form a ramp up which the carton can be pushed by the movement of tray . the exemplary fingers each also have a conveyor belt 252 for transferring the cartons to the conveyor 242 . each finger may also include a strut 258 ( fig1 ) supporting the wedge and at least partially supporting the associated conveyor 252 . a platform 260 may replace or span the struts at a height sufficiently above the conveyor 240 to allow the trays to pass below a leading edge 262 of the platform . the exemplary wedges have sufficient length so that the movement of the tray will drive the cartons up the wedges until the bottom surface of a leading portion of the carton comes into engagement with some or all of the conveyor belts 252 . a small carton may be pushed forward and up the ramp ( formed by the wedges / tips ) primarily by friction between the bottom of the carton and the tray . the notches 44 in the ridges in the tray bottom are provided to supplement this friction and the rear / trailing end wall of the tray acts as a positive stop should the carton slide on the tray and not be captured by the notches . for a relatively large carton ( e . g ., one that longitudinally fills the tray ) the engagement may merely be with the rear / trailing end wall . as the carton is pushed far enough onto conveyor belts 252 by the motion of tray , a point is reached wherein the friction between belts and the bottom surface of carton is sufficient for the carton to be moved by belts without regard to the motion of the tray and the carton is pulled away from the tray . this may offer a benefit over prior systems by placing the point at which control of the carton passes from the tray to the carton removal apparatus earlier in the removal process . extending the belts 252 through the slots 40 reaching below the top of the end wall of the tray and into the interior space of the tray may facilitate this . fig1 shows that each strut member 258 extending from a common drive shaft 270 at the carton output end to an idler pulley 272 ( fig1 ) at the intake end where the wedge / tip is attached . each strut holds its wedge / tip in position and additionally provides support for its belt as the assembly of belts supports the weight of the carton . a motor 274 and its connection with shaft 27 may be standard items typically used in conveyors . trays arrive at the apparatus on the conveyor 240 . this conveyor is an item that is presently available from one or more sources and is of the type that , as it conveys the tray , also moves the tray to the right relative to the direction of travel so that the tray is in contact with the side wall 204 of the conveyor when it arrives at the tray unloading machine . this ensures a predictable positioning of the tray as it approaches the unloading machine , thus aligning the slots in the end of the tray with the wedges so that the wedges can enter the slots . the assembly of conveyor belts 252 is powered by the motor 274 acting through the shaft 220 such that the belts move in the same direction as the conveyor mechanism 240 and they move at a speed that is generally equal to or greater than that of the conveyor 240 . trays containing cartons arrive at the unloading machine on conveyor 240 . after a carton is removed from a tray , the unloading machine moves the carton onto the conveyor 242 . empty trays continue on the conveyor 240 . the exemplary conveyor 240 is generally horizontal and conveyor 242 is on an incline leading up and away from the unloading machine . alternative embodiments could vary such that the conveyor 240 slopes downward into the unloading machine with the conveyor 242 being generally level , or could also be such that both conveyors are on an incline or both are horizontal . in use , the tray unloading machine operates in an unattended fashion and enables the following process . trays containing cartons approach the apparatus on a conveyor . each tray may be one of multiple predetermined sizes and the carton carried by the tray can vary in size and weight . additionally , either end of the tray can approach the apparatus first . without interrupting the continuous motion of the carton , the apparatus removes the carton from the tray , allowing the now empty tray to continue in motion and it moves the carton onto a separate conveyor for continued processing . one or more embodiments of the present invention have been described . nevertheless , it will be understood that various modifications may be made without departing from the spirit and scope of the invention . for example , when applied to different existing warehouse environments ( e . g ., conveyor systems , etc ) details of such environments will influence details of any particular implementation . accordingly , other embodiments are within the scope of the following claims .