  We extend one dimensional asymmetric simple exclusion process (ASEP) to a
surface and show that the effect of transverse diffusion is to induce a
continuous phase transition from a constant density phase to a maximal current
phase as the forward transition probability $p$ is tuned. The signature of the
nonequilibrium transition is in the finite size effects near it. The results
are compared with similar couplings operative only at the boundary. It is
argued that the nature of the phases can be interpreted in terms of the
modifications of boundary layers.
