It is well documented that the concentrations of highly volatile group V atoms in liquid droplets catalyzing the vapor-liquid-solid growth of III-V nanowires decrease in the quasi-instantaneous process of monolayer progression and can even drop to equilibrium at a stopping size. This effect has far-reaching implications in the nanowire morphology, crystal phase, and nucleation statistics but was never considered in the compositional modeling of ternary nanowires. Here, we present the first attempt of such modeling for wurtzite III-V nanowires based on group V intermix. We show that the liquid-solid distribution of such nanowires starts from the kinetics shape at nucleation and transitions to the equilibrium distribution at the stopping size. The vapor-solid distribution is fully determined by the initial liquid composition at nucleation and is reduced to a simple analytic shape under some reasonable assumptions. When the stopping size is smaller than the nanowire monolayer, our theory predicts spatially inhomogeneous composition across the nanowire axis. The model fits very well the available compositional data on InPxAs1-x, GaPxAs1-x, and InSbxAs1-x nanowires grown with different catalysts and sheds more light on the compositional control over III-V ternary nanowires in general. These results provide a starting point for further advancements in understanding and modeling of the complex growth process with a time-scale hierarchy of quasi-instantaneous monolayer progression and slow refill from vapor.