We study the phase behavior of model colloidal systems composed of infinitely thin hard platelets, with polydispersity in the size of the particles. Semi-grand Gibbs ensemble simulations are used to study the coexisting nematic and isotropic phases for a range of systems with varying polydispersity. Particle size segregation is observed in the two coexisting phases, with the larger particles tending to be found in the nematic phase. This fractionation becomes more evident with increasing polydispersity. We examine the relationship between the size of a particle and its orientation in the nematic phase and find that the larger particles tend to be more orientationally ordered than the smaller ones. The coexistence densities determined from the simulations are compared to those obtained from recent experiments on colloidal platelets.