Before revision:  We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the distribution is non-monotonic provided the motor processivity is sufficiently small .
After revision:  We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the distribution is non-monotonic with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay .