We report first-principles calculations based on the density-functional theory that clarify atomic reactions of ammonia decomposition and subsequent nitrogen incorporation during GaN epitaxial growth. We find that Ga-Ga weak bonds are ubiquitous on Ga-rich growing surface and responsible for the growth reactions. Furthermore, Car-Parrinello Molecular Dynamics simulations predict the existence of 2-dimensional Ga liquid phase, providing new insight into the epitaxial growth. The obtained results are expected to become basics for multiscale growth simulations in future.