Abstract In this work, we revisit models of the diffusion-induced growth of nanowires (NWs) accompanied by the growth of crystalline layers on the nonactivated areas of the substrate surface. In the conventional approach, the presence of the surface steps is taken into account implicitly by introducing effective diffusion length of adatoms before desorption or incorporation. In contrast, here we treat adatom incorporation as an outcome of a sequence of elementary surface processes on the terraces and step edges. The surface diffusion problems are formulated and solved for two modes of the lateral growth at the substrate surface: (i) submonolayer growth of 2D islands and (ii) permanent presence of the steps forming a closed loop around the NW base. In the limiting cases where the substrate adatoms with high probability either reach the sidewall of a NW or leave the substrate surface by desorption or attachment to 2D islands, our analysis demonstrates the correspondence between this approach and the conventional one under the relevant and physically transparent choice of the effective diffusion length. It has been shown that at relatively large NW heights the steps act as the sinks not only for the atoms impinging the substrate surface but also for the atoms impinging the NW sidewalls. This explains the failure of the simple material balance arguments to predict the NW height evolution observed in the experiments on the Au-assisted growth of InAs and GaAs NWs.