We use the grand canonical Monte Carlo method to study the nature of wettin
g transitions on a variety of heterogeneous surfaces. The model system we e
xplore, Ne adsorption on Mg, is one for which a prewetting transition was f
ound in our previous simulations. We find that the first order transition p
resent on the flat surface is absent from the rough surface. Nevertheless,
the resulting isotherms are, in some cases, so close to being discontinuous
that the distinction would be difficult to discern in most experiments.