Quarkonium production in ultra-relativistic nuclear collisions: suppression vs. enhancement

After a brief review of the various scenarios for quarkonium production in ultra-relativistic nucleus-nucleus collisions we focus on the ingredients and assumptions underlying the statistical hadronization model. We then confront model predictions for J/$\psi$ phase space distributions with the most recent data from the RHIC accelerator. Analysis of the rapidity dependence of the J/$\psi$ nuclear modification factor yields first evidence for the production of J/$\psi$ mesons at the phase boundary. We conclude with predictions for charmonium production at the LHC.