Due to the large band-gap bowing associated with low N contents in III-V semiconductors, ternary and quaternary dilute nitride alloys have sparked interest over the last years for a wide range of technological applications. However, the realization of these alloys has been hampered by several challenges such as the extremely low equilibrium solubility of N and composition fluctuations. In order to overcome these challenges a detailed understanding of the growth of these alloys at the atomic level is crucial. Therefore, by employing state-of-the art first-principles calculations, this work...