This study presents numerical modeling based on a relatively limited number of gas-phase and surface reactions to simulate the growth rate of aluminum nitride layers on AlN templates and c-plane sapphire in a broad range of deposition parameters. Modeling results have been used to design particular experiments in order to understand the influence of the process parameters on the crystal quality of AlN layers grown in a high-temperature hydride vapor-phase epitaxy process fed with NH3, AlCl3, and H-2. Modeling results allow to access to very interesting local quantities such as the surface site ratio and local supersaturation. The developed universal model starting from local parameters might be easily transferred to other reactor geometry and process conditions. Among the investigated parameters (growth rate, temperature, local supersaturation, gas-phase N/Al ratio, and local surface site N/Al ratio), only the growth rate/supersaturation or growth rate/temperature relationships exhibit a clear process window to use in order to succeed in growing epitaxial AlN layers on c-plane sapphire or AlN templates. Gas-phase N/Al ratio and local surface site N/Al ratio seem to play only a secondary role in AlN epitaxial growth