The continuous evolution from a random crystalline orientation (near the substrate) towards a definite texture (near the outer surface), established in the previous paper for PVD TiN coatings, was modelled quantitatively. The tendency for the smallest possible surface energy was considered as the driving force for the texture evolution. The experimental trends observed in the texture evolution could be reproduced, using realistic parameters. From an analytical treatment simple expressions for crucial characteristics of the texture evolution could be obtained, as for instance for the typical time (or thickness) at which the system will switch from a random to a peaked distribution, and for the time dependence of the spread of the orientational distribution of the crystallites in the growing film.