It has been claimed that graphene growth on copper by chemical vapor deposition is dominated by crystallization from the surface initially supersaturated with carbon adatoms, which implies that the growth is independent of hydrocarbon addition after the nucleation phase. Here, we present an alternative growth model based on our observations that oppose this claim. Our Gompertzian sigmoidal growth kinetics and secondary nucleation behavior support the postulate that the growth can be controlled by adsorption-desorption dynamics and the dispersive kinetic processes of catalytic dissociation and dehydrogenation of carbon precursors on copper.