Convection due to electric and gravity forces increase complexity in thin layer electrochemistry (ECD). We describe conditions in a vertical cell with the cathode above the anode in which global convection is eliminated and a dense branched morphology with a smooth front is obtained. It is shown that these conditions allow a theoretical one dimensional modeling notably simplifying the complex analysis of the problem. We report experimental measurements under constant current conditions showing that the deposit, cathodic and proton fronts scale linearly with time, a signature of migration controlled regime. We discuss a theoretical ECD model under galvanostatic conditions with a three ion electrolyte and a growth model, consisting in the one dimensional Nernst-Planck equations for ion transport, the Poisson equation for the electric field and a growth law whose front velocity equals the anion mobility times the local electric field. The model predicts cation, anion and proton concentration profiles, electric field variations and deposit growth speed, that are in good agreement with experiments; the predicted evolution and collision of the deposit and proton fronts reveal a time scaling close to those observed in experiments. (C) 2007 Elsevier Ltd. All rights reserved.