Even in thin horizontal cells, electrodeposition of tree-like metal aggregates is accompanied by a gravity-induced fluid flow at the electrodes. This flow has been calculated and the resulting map of the salt concentration has been deduced. Two extreme flow regimes are found : at shorter times, fluids with different densities behave as immiscible liquids and the extent of the perturbed zone near the electrode is found to vary with time as t(4/5). For longer times, fluid motion is sufficiently slow that diffusion tends to equalize the concentrations vertically (i.e. along the direction normal to the cell). In this regime, the extent of the perturbed zone varies as t(1/2). These two types of behaviour account quantitatively for experimental measurements on Cu electrodeposition in copper sulphate electrolytes.