Catalyst-free growth of III-V nanowires enables different optoelectronic applications though usually requires substrate patterning to control the size and position of nanowires. However, the impact of substrate modification on the nanowire nucleation is not well-understood yet. The theoretical approach of this work studies the effect of substrate boundaries and adatom diffusion on the nucleation rate of catalyst-free III-V NWs on substrates with circularly symmetric patterning. In the model results, we distinguish and demonstrate four different scenarios of nanowire nucleation, depending on the properties of the patterned and unpatterned surfaces.