We use ab initio calculations to determine the preferred nucleation sites and migration pathways of Ti, Al and N adatoms on cubic NaCl-structure (B1) AlN surfaces, primary inputs towards a further thin film growth modelling of the TiAlN alloy system. The potential energy landscape is mapped out for both metallic species and nitrogen adatoms for two different AlN surface orientations, (001) and (110), using density functional theory. For all species, the adsorption energies on AlN(011) surface are larger than on AlN(001) surface. Ti and Al adatom adsorption energy landscapes determined at 0 K by ab initio show similar features, with stable binding sites being located in, or near, epitaxial surface positions, with Ti showing a stronger binding compared to Al. In direct contrast, N adatoms (Nad) adsorb preferentially close to N surface atoms (Nsurf), thus forming strong N2-molecule-like bonds on both AlN(001) and (011). Similar to N2 desorption mechanisms reported for other cubic transition metal nitride surfaces, in the present work we investigate Nad/Nsurf desorption on AlN(011) using a drag calculation method. We show that this process leaves a Nsurf vacancy accompanied with a spontaneous surface reconstruction, highlighting faceting formation during growth.