Aluminum nitride (AlN), gallium nitride (GaN) and indium nitride (InN) form a family of technologically important semiconductors of high importance to light-emitting diodes and high frequency electronics. Although thin films of these materials are routinely manufactured by chemical vapor deposition (CVD) and atomic layer deposition (ALD), the methods are far from optimal and knowledge of the underlaying chemical processes are lacking. In this work we performed ab-initio investigations of the surface coverage of these materials under an ammonia rich atmosphere. Periodic density functional theory (DFT) calculations were used to test probable surface structures, their electronic and thermal energies were used to calculate their contribution to the surface composition at temperature and pressure conditions relevant for CVD and ALD processes of these materials. The results show similarities between the group of materials with similar NHx surface structure present for all three. Comparison of the coverage showed that at low growth temperatures the surface is expected to be covered by NH2 while at high temperatures most surface sites would be vacant. The surface structures where all found to be most stable on AlN and least stable on InN. These results are important for further investigations of the material growth mechanisms.