  We provide a quantitative picture of non-conserved interface growth from a
diffusive field making special emphasis on two main issues, the range of
validity of the effective small-slopes (interfacial) theories and the interplay
between the emergence of morphologically instabilities in the aggregate
dynamics, and its kinetic roughening properties. Taking for definiteness
electrochemical deposition as our experimental field of reference, our
theoretical approach makes use of two complementary approaches: interfacial
effective equations and a phase-field formulation of the electrodeposition
process. Both descriptions allow us to establish a close quantitative
connection between theory and experiments. Moreover, we are able to correlate
the anomalous scaling properties seen in some experiments with the failure of
the small slope approximation, and to assess the effective re-emergence of
standard kinetic roughening properties at very long times under appropriate
experimental conditions.
