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.