The evolution of the growth morphology of thin films of InN on (00.1) sapphire and on (00.1) sapphire prenudeated by a layer of AIN have been followed as a function of the thickness of the InN overlayer. The InN thin films and the AIN nucleation layers were deposited by reactive magnetron sputtering and first characterized by X-ray scattering, profilometry, and electrical transport. These AIN-nucleated InN films displayed heteroepitaxial grains, and high Hall mobility -even in the limit of InN overlayer on the order of 20-40Å. In parallel, InN films of varying thickness were grown directly onto (00.1) sapphire. These films showed a mixture of textured and heteroepitaxial grains, and lower Hall mobility. Atomic force and scanning tunneling microscopy studies have focussed on the morphology of the InN films with thicknesses: (a) much smaller than the AIN nucleation layer; and, (b) near the morphological transition that occurs at ∼1μm and has been attributed to the crossover from a 2D to a 3D growth mechanism. Additional correlations of X-ray structural coherence with growth mode are also examined.