We have studied the global phase diagram of a uniaxial nematic, modelled by a Lebwohl- Lasher Hamiltonian, in a slab geometry. Molecular-field and Bethe-type approximations have been used to determine the structural and thermodynamic properties of a system confined by walls that induce a perpendicular alignment. The latter approximation incorporates short-range correlations that are excluded from molecular-field theories. The critical behaviour of the system was analysed and we located the critical sizes and fields for which the bulk first-order transition becomes continuous in the film. Within the Bethe approximation we found that the critical transitions are destroyed for films with a thickness L⩾21. This is significantly higher than the value of 14 obtained using the mean-field approximation. The properties of thick films were also studied and in particular, we analysed the wetting behaviour and the temperature shift of the capillary first-order transitions. The results show that the Kelvin equation for the shift in the transition temperature is valid for L⩾70 when there is no wetting in the semi-infinite system. A global phase diagram of the model is presented.