Several available theoretical descriptions of the potentiostatic current transient that allow the determination of the rates of the nucleation process, A, and the number densities of sites for nucleation, N-0, with three-dimensional diffusion-controlled growth of clusters are critically examined and compared with experimental and computer-simulated data. All these obtain the overall current from the material flux to free, noninteracting growing centers, considering the overlap of circular diffusion zones expanding around them. It is shown that even though when compared to experimental data the diverse theories appear almost indistinguishable, essential differences among them arise from their distinct calculation of the growth rare of diffusion zones, yielding significantly different values for A and No. Computer simulations of the process for which the values of A and No are accurately known allowed meaningful comparisons between theories and an assessment of the relative accuracy with which the different available formulations yield estimates of the kinetic parameters.