We present a Monte Carlo simulation study of the phase behaviour and molecular organization of fullerene-based compounds, formed by a central fullerene with two mesogenic groups attached at its sides, that we describe with a generalized Gay–Berne model with flexible spacers. We consider two cases with identical substituents, either rod-like or disc-like, and investigate the thermotropic phases they form, focusing on the microsegregation and spatial organization of the fullerene and mesogen moieties, also in view of the potential interest for organic solar cells. The simulations produce, for these phases, equilibrium configurations with partial or complete two-dimensional segregation of C60 from mesogenic moieties. The predicted phase organisations seem very promising in terms of optimization of charge and energy transport properties.