  We present a complete study of the Multiparticle Biased Diffusion-Limited
Aggregation (MBDLA) model supplemented with surface difussion (SD), focusing on
the relevance and effects of the latter transport mechanism. By comparing
different algorithms, we show that MBDLA+SD is a very good qualitative model
for electrodeposition in practically all the range of current intensities {\em
provided} one introduces SD in the model in the proper fashion: We have found
that the correct procedure involves simultaneous bulk diffusion and SD,
introducing a time scale arising from the ratio of the rates of both processes.
We discuss in detail the different morphologies obtained and compare them to
the available experimental data with very satisfactory results. We also
characterize the aggregates thus obtained by means of the dynamic scaling
exponents of the interface height, allowing us to distinguish several regimes
in the mentioned interface growth. Our asymptotic scaling exponents are again
in good agreement with recent experiments. We conclude by discussing a global
picture of the influence and consequences of SD in electrodeposition.
