Brownian Dynamics (BD) simulations of instantaneous nucleation followed by diffusion-controlled growth of metal nanoparticles on surfaces have shown that a regular distribution of nucleation sites on the surface leads to a reduction in particle size dispersion. However, for several applications, the distribution of active sites on the surface is irregular and random. We use BD simulations to investigate the influence of surface reaction rate on the development of size dispersion of interfacial nanostructures that form by irreversible deposition of noninteracting particles onto surfaces with randomly distributed nucleation sites. The macroscopic balance between the surface reaction rate and bulk diffusion is incorporated into the BD simulations by using a reaction probability that approaches unity in the case of instantaneous, diffusion-limited deposition. It is found that the size uniformity of the growing particles on the randomly distributed active sites can be improved by decreasing the reaction probability. The overlap of diffusion zones surrounding the growing particles, referred to as interparticle diffusional coupling, is responsible for the particle size dispersion in diffusion-controlled growth on randomly distributed sites. The simulation results, in qualitative agreement with experiments, show that reducing the reaction probability is an effective means to reduce the interparticle diffusion coupling, and thereby reduce the particle size dispersion. This could be accomplished by manipulating the process variables that influence the surface reaction rate and/or the bulk diffusivity of the particles.