Methods are disclosed for making graft copolymers. The methods comprise the steps of: (a) providing (i) an ethylene/propylene (EP) copolymer or other graftable polymer, (ii) an ethylenically unsaturated sulfur-, nitrogen- and/or oxygen-containing monomer, and (iii) an amount of an initiator sufficient to graft said monomer and EP copolymer or other graftable polymer; (b) introducing said EP copolymer or other graftable polymer into an extruder; (c) introducing said monomer into the extruder; (d) introducing said initiator into the extruder; wherein at least one of the above-identified reactants in (a) is introduced in the presence of a polar solvent; and (e) reacting said EP copolymer or other graftable polymer, monomer and initiator by operating said extruder, thereby forming the graft copolymer. This invention also relates to methods of making a dispersant viscosity index improver and methods for making a lubricating oil. This invention further relates to graft copolymer products made by the aforementioned methods.