  The production of quarkonium in heavy ion collisions is studied at RHIC and
LHC energies. General arguments indicate that, due to initial production of
multiple quark pairs in each central collision, the final population of
quarkonium may exhibit significant enhancements over straightforward
extrapolation of behavior at SPS energy. Explicit calculations based on both a
statistical hadronization picture and a kinetic formation mechanism in a
deconfined state verify these general expectations. Such enhancements will
alter the nature of how quarkonium yields may be used as a signature of
deconfinement.
