Using the models proposed by Girifalco and by Ruoff and Hickman for describing the C 60 -C 60 and C 60 -graphite interactions, respectively, we have carried out a computer simulation study of the structures and phase changes of clusters of C 60 molecules supported on a graphite substrate. We have also analyzed the configurations and binding energies of layers of C 60 molecules deposited on the same substrate. It is predicted that the ground-state structures of the supported clusters consist in monolayerlike hexagonal arrangements parallel to the graphite surface, and that when the temperature is raised the supported fullerene clusters lose C 60 molecules by sublimation before they can attain a liquidlike state.