Fossil Groups Origins III. Characterization of the sample and
  observational properties of fossil systems
  (Abridged) Fossil systems are group- or cluster-sized objects whose
luminosity is dominated by a very massive central galaxy. In the current cold
dark matter scenario, these objects formed hierarchically at an early epoch of
the Universe and then slowly evolved until present day. That is the reason why
they are called {\it fossils}. We started an extensive observational program to
characterize a sample of 34 fossil group candidates spanning a broad range of
physical properties. Deep $r-$band images were taken for each candidate and
optical spectroscopic observations were obtained for $\sim$ 1200 galaxies. This
new dataset was completed with SDSS DR7 archival data to obtain robust cluster
membership and global properties of each fossil group candidate. For each
system, we recomputed the magnitude gaps between the two brightest galaxies
($\Delta m_{12}$) and the first and fourth ranked galaxies ($\Delta m_{14}$)
within 0.5 $R_{{\rm 200}}$. We consider fossil systems those with $\Delta
m_{12} \ge 2$ mag or $\Delta m_{14} \ge 2.5$ mag within the errors. We find
that 15 candidates turned out to be fossil systems. Their observational
properties agree with those of non-fossil systems. Both follow the same
correlations, but fossils are always extreme cases. In particular, they host
the brightest central galaxies and the fraction of total galaxy light enclosed
in the central galaxy is larger in fossil than in non-fossil systems. Finally,
we confirm the existence of genuine fossil clusters. Combining our results with
others in the literature, we favor the merging scenario in which fossil systems
formed due to mergers of $L^\ast$ galaxies. The large magnitude gap is a
consequence of the extreme merger ratio within fossil systems and therefore it
is an evolutionary effect. Moreover, we suggest that at least one candidate in
our sample could represent a transitional fossil stage.
