  We study the interface dynamics of a discrete model to quantitatively
describe electrochemical deposition experiments. Extensive numerical
simulations indicate that the interface dynamics is unstable at early times,
but asymptotically displays the scaling of the Kardar-Parisi-Zhang universality
class. During the time interval in which the surface is unstable, its power
spectrum is anomalous; hence the behaviors at length scales smaller than or
comparable with the system size are described by different roughness exponents.
These results are expected to apply to a wide range of electrochemical
deposition experiments.
