We further extend these works by comparing the possible adsorbate-surface structures in the whole family of 13Ns as well as employing a statistical mechanical approach investigate the mixing of the different surface-coverage structures and view the dependence of the mixing on temperature, gas mixture and pressure. We find that the most probable surface NHx specie at low temperatures is the on-top NH2 for AlN, GaN and InN. At high temperatures, no NHx species are stable on the surface and will desorb, leaving a bare surface. The transition temperatures between these two follows a clear trend where AlN has the highest transition temperature and InN the lowest with GaN in between.