The primary current distribution for electrodeposition onto a surface composed of a perfectly conducting section and. a highly resistive section is examined, both by direct numerical calculation and by singular-perturbation analysis. Results of the study show how the current density and the region over which electrodeposition reactions are appreciable scale with the conductivity and thickness of the resistive section of the electrode. The perturbation analysis leads to an approximate expression (Eq. 34 in text) for the front velocity of a growing metallic film, a result which is of practical interest for design estimates of the speed of coverage in metallization processes on resistive substrates.