A cationic copolymer is obtained by the Hofmann rearrangement (also referred to as the Hofmann degradation reaction) in aqueous solution in the presence of an alkaline-earth and/or alkali hydroxide and an alkaline-earth and/or alkaline hypohalide, on a base copolymer comprising at least one nonionic monomer selected from the group comprising acrylamide (and/or methacrylamide), N,N-dimethylacrylamide and/or acrylonitrile The copolymer is branched after the Hofmann rearrangement, in the presence of at least one polyfunctional branching agent, and is soluble in water.