  We propose a simple and versatile model to understand the deviations from the
well-known Kolmogorov-Johnson-Mehl-Avrami kinetics theory found in metal
recrystallization and amorphous semiconductor crystallization. We analyze the
kinetics of the transformation and the grain size distribution of the product
material, finding a good overall agreement between our model and available
experimental data. The information so obtained could help to relate the
mentioned experimental deviations due to preexisting anisotropy along some
regions, to certain degree of crystallinity of the amorphous phases during
deposition, or more generally to impurities or roughness of the substrate.
