A graft copolymer is prepared by a process comprising: graft polymerizing a polyamide-forming monomer selected from the group consisting of lactams and .omega.-aminocarboxylic acids and an oligocarboxylic acid selected from the group consisting of from 0.015 to about 3 mol. % of dicarboxylic acid and from 0.01 to about 1.2 mol. % of tricarboxylic acid, in each case the stated amounts of oligocarboxylic acid based on a molar amount of lactam, .omega.-aminocarboxylic acid or combination thereof, onto from 0.5 to 25% by weight, based on the graft copolymer, of a polyamine having at least 11 nitrogen atoms and a number-average molecular weight M.sub.n of at least 500 g/mol., wherein the amino group concentration in the graft copolymer ranges from 100 to 2500 mmol./kg.