Structures and energies of different NHx surface structures on the three 13Ns, AlN, GaN and InN were investigated by DFT. Their stability at different temperature and pressures were determined by a minimization of the systems Gibbs energy. We have shown that the surface terminations are dependent on temperature with a hydrogen bonding NH2(tp) surface structure being the dominating structure at low temperatures and a bare surface being dominating at high temperatures for all three 13Ns. The NH2(tp) surface structure forms a good candidate for growth of 13Ns films since the availability of lone electrons pairs on the surface nitrogen can act as adsorption sites for a metal precursor containing a Lewis-acidic metal-atom. We also show that stability of the nitrogen containing surface structures decreases as the atomic number of the metal moves downwards in group 13, indicating that the growth process would be easier on AlN compared to GaN and hardest on InN, in agreement with experimental findings. The obtained structures can also be used to further develop models to investigate the atomistic processes during CVD and ALD growth as a basis for the adsorption mechanics of a metal precursors.