Through the use of a population balance equation (PBE), the nucleation and growth of nanocrystals evolving under various initial reaction conditions are simulated. Simulations of nanocrystal (NC) growth in both the diffusion and reaction limits are presented, and it is concluded that NC growth proceeds under strongly reaction-limited kinetics. The particle size distributions obtained in the asymptotic diffusion and reaction limits were found to be slightly narrower than the stationary distributions predicted by LSW and Wagner theories, respectively. There is strong experimental evidence indicating that the early stages of NC synthesis involve simultaneous nucleation, growth and coarsening. The simulations performed here are able to replicate these conditions, providing insight into the factors that govern these early time processes, as well as the consequences they have at longer reaction times.