  We review the statistical hadronization picture for charmonium production in
ultra-relativistic nuclear collisions. Our starting point is a brief reminder
of the status of the thermal model description of hadron production at high
energy. Within this framework an excellent account is achieved of all data for
hadrons built of (u,d,s) valence quarks using temperature, baryo-chemical
potential and volume as thermal parameters. The large charm quark mass brings
in a new (non-thermal) scale which is explicitely taken into account by fixing
the total number of charm quarks produced in the collision. Emphasis is placed
on the description of the physical basis for the resulting statistical
hadronization model. We discuss the evidence for statistical hadronization of
charmonia by analysis of recent data from the SPS and RHIC accelerators.
Furthermore we discuss an extension of this model towards lower beam energies
and develop arguments about the prospects to observe medium modifications of
open and hidden charm hadrons. With the imminent start of the LHC accelerator
at CERN, exciting prospects for charmonium production studies at the very high
energy frontier come into reach. We present arguments that, at such energies,
charmonium production becomes a fingerprint of deconfinement: even if no
charmonia survive in the quark-gluon plasma, statistical hadronization at the
QCD phase boundary of the many tens of charm quarks expected in a single
central Pb-Pb collision could lead to an enhanced, rather than suppressed
production probability when compared to results for nucleon-nucleon reactions
scaled by the number of hard collisions in the Pb-Pb system.
