It is confirmed that it is possible to obtain a mathematical solution to the problem of the nucleation and three-dimensional growth at constant potential of single growth centres of a new phase on a microelectrode substrate under all conditions ranging from kinetic to diffusion control of the growth process under the assumption that diffusion is in a quasi-steady state. The results are extended to double-potential-step experiments and it is shown that similar complete descriptions can be derived for experiments where the growth centre acts as a catalyst site for an electrocatalytic reaction. Cyclic voltammetry of the two types of processes is discussed for a more restricted range of conditions, namely pure kinetic or diffusion control of the growth of the catalyst centre. It is shown that it should be possible to detect catalytic reactions at a single atom of the new phase.