Ag/Cu (0 0 1) electrodeposition is studied in the framework of an atomistic kinetic model handled by Monte Carlo simulations. When the kinetics are controlled by a nucleation and growth process, the Kolmogorov-Johnson-Mehl-Avrami (KJMA) formalism is able to reproduce it. The classical nucleation theory allows one to relate the physical quantities involved in the KJMA equation to the microscopic parameters of the kinetic model. However, to obtain a quantitative agreement with Monte Carlo simulations, the morphology of the clusters, in particular the concentration of kinks, and their degeneracy must be taken into account. This improves the calculation of the edge free energy and the description of the frequencies of attachment and detachment of monomers. This leads to a good agreement with MC simulations in a large range of temperatures for the kinetics of electrodeposition and for the physical quantities that control it, i.e., the steady-state nucleation rate, the asymptotic growth rate and the incubation time. (C) 2003 Published by Elsevier B.V.