A new stochastic model has recently been developed, which describes the heterogeneous nucleation in electrolytic cells when the deposition process is controlled by diffusion. The calculated expressions for current transients are able to describe the electrodeposition of cobalt thin films on silicon substrates. However, in a large number of real situations the electrochemical process of multiple nucleation and growth is not exclusively controlled by diffusion. In this work, the former model is extended to include the rate at which chemical reactions occur. The reaction rate affects the overall process and the resulting current emerges as a consequence of the interplay between mass transport (diffusivity) and reaction kinetics. The improvement of the model enables one to consider in detail this more general case. where both mechanisms coexist, and to analyze the competition between them. The theoretical predictions obtained with this general model are also compared with experimental data.