  We present new results on the statistical hadronization of heavy quarks at
SPS, RHIC and LHC energies. Several new aspects are considered, among them a
separation of the collision geometry into a ``core'' and a ``corona'' part and
an estimate of the annihilation rate of charm quark in a hot plasma, together
with a critical assessment of its influence on the results. For RHIC energies
we investigate the centrality dependence of J/psi production focusing on the
model results for different values of the charm production cross section,
including its theoretical and experimental uncertainty. We also study, within
this model, the rapidity dependence of the J/psi yield. Recent RHIC data from
the PHENIX experiment are well reproduced. At LHC energy, we update our model
predictions for the centrality dependence of the J/psi yield and investigate as
well the rapidity dependence. We also discuss the transverse momentum
distributions of J/psi mesons expected from the model and provide predictions
for a range of values of the expansion velocity at chemical freeze-out.
Finally, we extend the model to predict Upsilon yields in Pb+Pb collisions at
LHC energy.
