mixtures [65] is that we do not find N - N coexistence ending in a lower critical point, at least not for the range of densities and size ratios that we explored. Similar results to ours, where N - N coexistence ends in an upper critical point were obtained using Onsager theory for mixtures of thick and thin rods [27]. This system of rods also displays isotropic-isotropic phase coexistence at high enough values of the diameter ratio, which we do not find to be stable in the present study. We have studied the bulk phase behaviour of binary mixtures of hard platelets, including isotropic and nematic states. The platelets are assumed to have circular shape and vanish- ing thickness. We have not considered positionally ordered phases such as columnar and crystalline phases, which are not expected to occur for the present model of particles with zero volume and zero packing fraction. Note that a first order N - Col transition was found at non-zero packing fraction in the limit of vanishing thickness [66]; simulations in this limit are possible because the model can be mapped onto a system of particles with finite volume but variable shape. Also, platelets with non-zero thickness exhibit a N - Col transition [67]; this was also reported for the Zwanzig model [35]. For a variety of size ratios, we have compared the results of Onsager theory and FMT. In the monodisperse limit we find that Onsager theory overestimates the I - N transition densities and predicts a larger biphasic gap than FMT; the results for FMT in this limit compare quantitatively well with those from simulation. Both theories predict a first order I - N phase transition. We expect that Onsager theory overestimates the density jump at coexistence and also overestimates the size of the biphasic gap. The FMT results show the appearance of re-entrant phenomena at a lower size ratio than for Onsager theory. FMT results also show a larger range of compositions for which N - N demixing at a given size ratio occurs. The N - N demixing occurs at λ = 2, where it is closed by an upper critical point. For λ ≥ 2 . 5 there is no critical point up to the densities we consider. In an experimental system of platelets with nonzero volume, one would expect a positionally ordered phase to be favoured before any possible remixing into a homogeneous nematic phase. We also examine the degree of nematic ordering along the phase boundaries for a selection of size ratios up to λ = 2 where N - N demixing ends in an upper critical point. The partial nematic 22 IV. CONCLUSIONS AND OUTLOOK