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The invention relates to a cationic (co)polymer obtained by means of a Hofmann degradation reaction in aqueous solution in the presence of an alkali and/or alkaline-earth hydroxide and an alkali and/or alkaline-earth hypohalide on a base (co)polymer containing at least one nonionic monomer selected from the group comprising acrylamide (and/or methacrylamide), N, N dimethylacrylamide and/or acrylonitrile, characterised in that it is branched after the Hofmann degradation reaction, in the presence of at least one polyfunctional branching agent, and in that it is soluble in water.