Polyelectrolyte adsorption onto surfaces is widely employed in water treatment and mining. However, little is known of the relative interaction strengths between surfaces and polymer. This fundamental property is assumed to be dominated by electrostatics, i.e., attractive interactions between opposite charges, which are set by the overall ionic strength ("salt concentration") of the solution, and charge densities of the surface and the polymer. A common, counterintuitive finding is a range of salt concentrations over which the amount of adsorbed polyelectrolyte increases as electrostatic interactions are tempered by the addition of salt. After an adsorption maximum, higher salt concentrations then produce the expected gradual desorption of polyelectrolyte. In this work, the salt response of the adsorption of the same narrow molecular weight distribution polycation, poly(N-methyl-4-vinylpyridinium), PM4VP, to a variety of surfaces was explored. Oxide powders for adsorption included Al2O3, SiO2, Fe2O3, Fe3O4, TiO2, ZnO, and CuO. Planar surfaces included silicon wafers, mica, calcium carbonate, and CaF2 single crystals. The PM4VP was radiolabeled with 14C so that sensitive, submonolayer amounts could be detected. The position of the peak maximum, or the lack of a peak, in response to added salt was used to rank the electrostatic component of the interaction. The importance of charge regulation, a shift in the surface pKa in response to solution species, was highlighted as a mechanism for adsorption on the "wrong" side of the isoelectric point and also as a factor contributing to the difficulty of reaching the totally desorbed state even at the highest salt concentrations.