  We investigate J/\psi transverse-momentum (p_t) distributions and their
centrality dependence in heavy-ion collisions at SPS and RHIC within the
framework of a two-component model, which includes (i) primordial production
coupled with various phases of dissociation, (ii) statistical coalescence of c
and \bar{c} quarks at the hadronization transition. The suppression of the
direct component (i) is calculated by solving a transport equation for J/\psi,
\chi_c and \psi' in an expanding fireball using momentum dependent dissociation
rates in the Quark-Gluon Plasma (QGP). The coalescence component is inferred
from a kinetic rate equation with a momentum dependence following from a blast
wave approach. At SPS energies, where the direct component dominates, the
interplay of Cronin effect and QGP suppression results in fair agreement with
NA50 p_t spectra. At RHIC energies, the p_t spectra in central Au+Au collisions
are characterized by a transition from regeneration at low p_t to direct
production above. At lower centralities, the latter dominates at all p_t.
