the invention relates to an apparatus for extruding a polymer profile directly onto the surface of a glass plate and particularly along a peripheral edge thereof . the extruded polymer profile is provided with a sealing and centering lip located on and projecting over the circumferential peripheral surface of the glass plate . the extrusion die has at least one supply channel for the polymer to be extruded . one supply channel or portion thereof leads the polymer material substantially to the portion of the die orifice directed toward the center of the plate . the other supply channel essentially supplies the portion of the orifice directed toward the outside . the supply channel may be provided with a shutoff device which regulates the volume flow . the regulation of the shutoff device takes place as a function of the radius of curvature of the path covered by the extrusion die .