III-V nitrides are intensely researched fur optoelectronic applications spanning the entire visible spectrum. Tn spite of realization of commercial devices and advances in processing of materials and devices, the understanding of the processing and epitaxial growth of these materials is incomplete. In this study, a rate equation approach is proposed based on physically sound surface processes to investigate the molecular bean epitaxy growth of GaN using ammonia. A surface riding layer of Ga and ammonia and its associated dynamics such as incorporation of Ga and N in to the crystal and desorption are included in the model. Rates of all surface processes are assumed Arrhenius type. The simulated Ga incorporation rate as a function of ammonia pressure and substrate temperature are in excellent agreement with the experimental data. Ga incorporation increases with increasing NH3 overpressure and saturates at a maximum value at large NH3 overpressure. The Ga incorporation rate exhibits a peak at 820 degrees C due to competition between thermally activated pyrolysis of NH3 and reevaporation of Ca from the surface. The simulated Ga desorption parameter versus time data is also in good agreement with the experimental data. These observations will be explained based on the inter-play of competing surface processes such as evaporation and incorporation.