Attachment of the peroxide initiator of radical polymerization to the surface of various oxides due to the adsorption of reactive copolymers of peroxide monomer and maleic anhydride (PM-MA) was performed. Plateau adsorption amount of PM-MA depend mainly on the nature of the solvent. It was found that adsorption is irreversible with respect to the solvent. Measuring the exchange between the polymer in the adsorbed layer and in solution, with the aid of a labeled polymer, it was shown that adsorption is reversible with respect to the polymer. Studying the competitive adsorption of PM-MA with some other polymers showed that PM-MA, because of its high adsorption ability, could not be replaced by another polymer, but it could replace another polymer from the adsorbent surface. A wetting technique was used to assess the behaviour of the polymer covering formed with PM-MA.