In LaMer burst nucleation, the individual nucleation events happen en masse, quasi-simultaneously, and at nearly identical homogeneous conditions. These properties make LaMer burst nucleation important for applications that require monodispersed particles and also for theoretical analyses. Sugimoto and co-workers predicted that the number of nuclei generated during a LaMer burst depends only on the solute supply rate and the growth rate, independent of the nucleation kinetics. Some experiments confirm that solute supply kinetics control the number of nuclei, but flaws in the original theoretical analysis raise questions about the predicted roles of growth and nucleation kinetics. We provide a rigorous analysis of the coupled equations that govern concentrations of nuclei and solutes. Our analysis confirms that the number of nuclei is largely determined by the solute supply and growth rates, but our predicted relationship differs from that of Sugimoto et al. Moreover, we find that additional nucleus size dependent corrections should emerge in systems with slow growth kinetics. Finally, we show how the nucleation kinetics determine the particle size distribution. We suggest that measured particle size distributions might therefore provide ways to test theoretical models of homogeneous nucleation kinetics.