We study the adsorption of strongly charged rod-like polyelectrolytes onto weakly oppositely charged surfaces in salt solutions by equating the chemical potentials between the bulk and adsorbed polyelectrolytes, and between the free and condensed ions along the rods. Lateral correlations between adsorbed polyelectrolytes lead to nonoverlapping cells of radius R, which we study as a function of salt concentration (s), surface charge densities (sigma), and polyelectrolyte charge density (1/b). We find a minimum in R and a maximum in the absolute value of the effective charge density of the surface-polyelectrolyte-ion system with increasing salt concentration. Charge inversion disappears in our model as the concentration of salt increases further. The critical salt concentration (s(c)) for polyelectrolyte adsorption scales as sigma(alpha) with alphaapproximate to1.8. We find differences between weakly and strongly charged polyelectrolyte adsorption. While s(c) decreases as b increases in weakly charged polyelectrolytes, it increases almost linearly with b in strongly charged polyelectrolytes. Similar adsorption trends are found in divalent salt solutions. More rods are adsorbed to neutralize the surface due to more rod charge neutralization in divalent salt solutions than in monovalent salt solutions. However, at high salt concentrations it is more difficult to totally desorb the chains (R=infinity) in monovalent salt than in divalent salt solutions. (C) 2003 American Institute of Physics.