We draw upon the theoretical methods developed in the preceding contribution to explore different mechanisms of island growth in the initial stages of the development of a thin film. In particular, we study the entropic consequences of assuming different sequences for generating a final nucleation pattern or island morphology on a finite, planar array. Our calculations lead to the conclusion that the most entropically favorable process for island growth is one in which the morphology is generated by a "row-filling" mechanism on a lattice with triangular geometry.