The nature and origin of the morphological instability which occurs in confined and unsupported electrodeposition experiments in galvanostatic regimes is discussed in terms of linear stability analysis, based on a theoretical work of Sundstrom and Bark.(1) The originality of our approach rests on the comparison of two-dimensional experimental concentration maps obtained by phase-shift interferometry with numerical simulations of the nonstationary evolution equations. We demonstrate both experimentally and theoretically that a morphological transition occurs when the concentration of reducible species approaches zero. We point out the relevance of the electroneutrality hypothesis for predicting the interfacial instability with reference to a destabilization mechanism, based on the existence of a space charge, proposed by Chazalviel.(2)