A process is provided according to the present invention comprising the steps of: functionalizing a base polymer by grafting alpha-beta unsaturated carboxylic acid, anhydride or ester to a base polymer, the base polymer being selected from the group of hydrogenated polymer of a conjugated diolefin and a copolymer of conjugated diolefins and monoalkenyl arenes, the grafting being performed in a blending device capable of imparting high mechanical energy and in the presence of 3 to 15 percent by weight, based on base polymer, of a suitable diluent oil; reacting the functionalized polymer with an amine; and recovering an animated polymer. This process results in a lower level of scission, crosslinking and coupling than processes which are essentially oil free. The product of this process is an excellent lubricating oil viscosity index improver and additionally has dispersant characteristics.