Recently, current vs voltage measurements have revealed a nonstandard behavior of the electric conductivity within some nematic liquid crystals (NLC) samples, and the results have been associated with the local orientational order at the free surfaces of the liquid crystal. We have used Monte Carlo simulation of a liquid crystal in a cell with two free surfaces at the opposite sides to understand how a local director imposed by free surfaces competes with the homeotropic alignment imposed by electrodes of the nematic cell.