Growth of polymer density in an electro-deposition model of polymer chains on an impenetrable wall is studied on a two dimensional discrete lattice using a Monte Carlo simulation. Polymer-polymer repulsion and polymer-wall attraction for the adsorbing wall (along with the neutral and repulsive interactions) are considered in an external field. Effects of the field strength (B), temperature (T), and chain length (L-c) on the density profile of the polymer chains and wall coverage are investigated. The spatial density profile shows onset of oscillation near the wall at a characteristic field (B-c) which depends on chain length and temperature, In low field, adsorption-co-desorption transition at the wall appear on increasing the temperature (unlike neutral and repulsive walls). In high field regime, on the other hand, a non-monotonic dependence of coverage on temperature is observed with a maximum at a temperature (T-m) which increases on increasing B. The equilibrium value of the polymer density (P-d) shows a power-law decay with the chain length, p(d) similar to L-c(-alpha), at the wall and in the bulk with corresponding values of the exponent alpha(w) and alpha(B); these exponents differ substantially and depend on B, T, and L-c. The coverage decays monotonically with the chain length at a constant temperature and field. (C) 1997 American Institute of Physics. [S0021-9606(97)51347-X].