A model of random birth and deterministic growth of monolayers formed on the facets of silver crystallites is presented, in which the edges are assumed to follow a propagation law and to decay over a finite distance which increases with increasing overpotential. This model is consistent with the potential dependence of the electrode impedance and with the current dependence of the power spectral density of the electrochemical noise measured for silver electrodeposition in nitrate or perchlorate solutions with an addition of tartaric acid. With increasing overpotential the delayed lengthening of the propagation distance allows the electrode activation and is at the origin of the low-frequency inductive response. The electrochemical noise is shown to originate not only from the random birth of edges but also from some low frequency fluctuations of another process.