A copolymer with stellate branching, of the general formula [A-].sub.k X, where A is the monovalent radical of a homopolymer, block copolymer or random copolymer of a conjugated diene and/or vinyl-aromatic hydrocarbon, k is a number from 1 to 10, and X is the k-valent radical of a coupling center produced by coupling with hexatriene, and the product of the hydrogenation thereof are described.