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 / ψ 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 / ψ 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 / ψ yield and investigate as well the rapidity dependence. We also discuss the transverse momentum distributions of J / ψ 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 ϒ yields in Pb + Pb collisions at LHC energy.