We report results from an experimental and modeling study of the far-from-equilibrium electrodeposition of Ni-Cu alloys by changing systematically the current density with focus on the surface structuring and surface content of the elements. General finding is that Cu prevails in the convex regions of the deposit, while Ni prevails in the concave ones. No deposition of a monophase is observed by the XRD analyses-in all samples are registered two phases under the form of solid solutions of Cu and Ni. With the increasing current density, the percentage of the major component increases towards deposition of pure Cu and Ni. Some oscillations of the overpotential with the current density are correlated with the Cu content in the Cu-rich solid solution. An original model based on Cellular Automata (CA) rationalizes the hypothesis that during their simultaneous deposition, Cu preserves the diffusion-limited growth mode, while the Ni discharges in a kinetically controlled one. The model is expected to be valid for lower current densities.