  Experiments with gold-gold collisions at RHIC have revealed (i) stronger
suppression of charmonium production at forward rapidity than at midrapidity
and (ii) the similarity between the suppression degrees at RHIC and SPS
energies. To describe these findings we employ the model that includes nuclear
shadowing effects, calculated within the Glauber-Gribov theory,
rapidity-dependent absorptive mechanism, caused by energy-momentum
conservation, and dissociation and recombination of the charmonium due to
interaction with co-moving matter. The free parameters of the model are tuned
and fixed by comparison with experimental data at lower energies. A good
agreement with the RHIC results concerning the rapidity and centrality
distributions is obtained for both heavy Au+Au and light Cu+Cu colliding
system. For pA and A+A collisions at LHC the model predicts stronger
suppression of the charmonium and bottomonium yields in stark contrast to
thermal model predictions.
