Abstract Within the lattice gas model for adsorption on cubic (100) surfaces, the effect of surface steps running along lattice directions is modelled by considering adsorption on terraces L lattice spacings wide, with various types of boundary energies on the right and left edges of the terrace. Both the cases of attractive and of repulsive nearest-neighbor interaction between the adparticles are considered. While adsorption isotherms are not much affected by boundary energies in the repulsive case, a drastic influence of various choices of boundary energies is identified for the case of attractive interactions, where the system separates in phases of low and high coverage, respectively. Then adsorption will occur typically near one of the terrace boundaries, and a “domain wall” separating the high and low coverage phases will run parallel to the steps. A wetting transition is identified between a phase where the domain wall is bound to one of the steps and a phase where it is “unbound”, delocalized in the bulk of the terrace. The phase diagram found in the simulation for this wetting transition agrees with a theoretical prediction due to Abraham. In contrast, for repulsive interactions where the system orders in the c(2 × 2) structure, antiphase boundaries occur which typically run perpendicular to the steps. The generalization of these results to other models as well as the application to experiments is briefly discussed.