The phase composition of HZO thin films is critical for the ferroelectric and electrical properties of the films and the devices they are integrated into. Optimization is a major challenge since the phase formation depends significantly on many influencing variables that are only partially understood so far. The Curie temperature is identified as an important parameter for understanding the behavior, since it depends sensitively on Zr content, the density of oxygen-related defects, layer thickness, and external stress. A two-step process, phase formation by pure kinetic transformation followed by nucleation, is proposed for phase formation. This is necessary because nucleation theory alone cannot explain the experimentally observed dependence on oxygen content. The classical nucleation model is modified at two crucial points. First, the polycrystalline structure is incorporated which allows the size effect to be implemented. Furthermore, the interface energies between the child and parent phase, which result from static ab initio calculations, are rescaled from dynamical effects. The resulting model is used to calculate the phase fractions during thermal processing. The results for the most important influencing variables are discussed and compared with experimental results. The causes of the undesired monoclinic phase are further analyzed.