Computer simulations are presented of the isotropic-to-nematic transition in a liquid crystal confined between two parallel plates a distance H apart. The plates are neutral and do not impose any anchoring on the particles. Depending on the shape of the pair potential acting between the particles, we find that the transition either changes from first-order to continuous at a critical film thickness H=Hx, or that the transition remains first-order irrespective of H. This demonstrates that the isotropic-to-nematic transition in confined geometry is not characterized by any universality class, but rather that its fate is determined by microscopic details. The resulting capillary phase diagrams can thus assume two topologies: one where the isotropic and nematic branches of the binodal meet at H=Hx, and one where they remain separated. For values of H where the transition is strongly first-order the shift DT of the transition temperature is in excellent agreement with the Kelvin equation. Not only is the relation DT~1/H recovered but also the prefactor of the shift is in quantitative agreement with the independently measured bulk latent heat and interfacial tension.