Theoretical analysis is presented for vapor-liquid-solid growth of III-V nanowires in the presence of three competing processes of the group V deposition, surface diffusion of group III adatoms and nucleation of islands at the liquid-solid interface. A generalized equation for the nanowire growth rate is obtained which can be limited of one of the three processes depending on the growth environment. Different regimes of vapor-liquid-solid growth of III-V nanowires are analyzed depending on the group III and V influxes and nanowire radius.