A fingering instability appears in thin-layer electrodeposition experiments from copper sulphate aqueous solutions in the presence of alkaline sulphates. In this case, cuprous oxide rich and highly space filling deposits are obtained. This latter characteristic allows them to manifest the hydrodynamic fingering instability of the concentration boundary layer that separates the copper depleted solution embedding the deposit from the bulk solution. Moreover, different dynamic morphological transitions experienced by these finger-like deposits are interpreted as due to proton and alkaline ion fronts.