We study a thin-film electrodeposition model that represents the relaxation of the deposited material by adatom diffusion on quenched crystal topographies and considers simple mechanisms of cation flux in the electrolyte. The results of numerical simulations with collimated flux and a rapid cation reduction in contact with the deposit relate the surface roughness and the adatom hop numbers with two model parameters. A comparison with the results of a collective diffusion model for vapor deposition shows differences in the surface morphologies but similarities in scaling relations, which suggest thermally activated (Arrhenius) forms for the parameters of the electrodeposition model and relate one of them to the applied current. Simulations with purely diffusive cation flux and possible pore formation in simple cubic lattices show the growth of self-organized structures with leaf shapes (dendrites) above a compact layer that covers the flat electrode. The thickness of this layer and the average dendrite size also obey scaling relations in terms of the model parameters, which predict that both sizes decrease with the applied current, in agreement with recent experimental studies. Under all flux conditions, an increase in adatom diffusivity with temperature implies an increase in the average sizes of low-energy surface configurations, independently of their particular shapes. Finally, we note that a previously proposed model for electrodeposition produced similar morphologies, but the quantitative relations for the characteristic sizes differ from those of the present model, which also advances with a consistent interpretation of temperature effects.