We present a new analytical approach for understanding and tuning the composition of ternary nanowires of III-V semiconductor compounds and interfacial abruptness of axial nanowire heterostructures in nucleation-limited regime of the vapor-liquid-solid growth. Binary nanowires of elemental semiconductors grown with any liquid catalyst present a simple particular case. The solid composition is first obtained as a function of the liquid composition by determining the saddle point of the island formation energy. This relationship is then used to obtain the compositional profiles across axial heterostructures in a kinetic treatment. Several ternary systems are considered including InGaAs, AlGaAs and InAsP. We find a new effect in InGaAs system which is due to strong interactions between solid InAs and GaAs and yields the miscibility gaps. This may help to form atomically sharp axial heterointerfaces in optimized growth recipes. Our results are consistent with earlier models and experimental data on GaAs/AlGaAs/GaAs nanowire heterostructures. Even more importantly, we formulate general routes for compositional design and obtaining sharp interfaces in different binary and ternary solid alloys. (C) 2017 Elsevier Ltd. All rights reserved.