A finely divided, cationic, aqueous polymer dispersion, wherein the mean particle size of the dispersed particles is from 5 to 250 nm, which is obtainable by emulsion polymerisation of ethylenically unsaturated monomers in an aqueous liquid containing a cationic prepolymer as a dispersant, wherein the cationic prepolymer is prepared in the presence of at least one polymerisation initiator by polymerisation of (a) from 15 to 45% by weight of at least one ethylenically unsaturated monomer comprising at least one quaternary ammonium group; (b) from 5 to 80% by weight of at least one optionally substituted styrene; (c) from 0 to 50% by weight of at least one C 1-12 alkyl (meth) acrylate; (d) from 0 to 10% by weight of at least one ethylenically unsaturated monomer comprising an acid group; (e) from 0 to 10% by weight of at least one ethylenically unsaturated monomer comprising an amine group; and (f) from 0 to 20% by weight of at least one non-ionic ethylenically unsaturated monomer differing from (b), (c) and (e), the sum of (a) + (b) + (c) + (d) + (e) + (f) being 100% by weight, in a first emulsion polymerisation in the presence of at least one non-ionic emulsifier, and thereafter, in the aqueous liquid containing the cationic prepolymer, a second emulsion polymerisation is carried out, in the presence of at least one polymerisation initiator, of a monomer mixture comprising (i) from 10 to 70% by weight of at least one of an optionally substituted styrene or (meth) acrylonitrile; (ii) from 30 to 90% by weight of at least one C 1-18 alkyl (meth) acrylate; (iii) from 0 to 30% by weight of at least one vinyl ester of linear or branched C 1-30 carboxylic acids; and (iv) from 0 to 30% by weight of at least one non-ionic ethylenically unsaturated monomer differing from (i), (ii) and (iii), the sum of (i) + (ii) + (iii) + (iv) being 100% by weight, and the first emulsion polymerisation and/or the second emulsion polymerisation is optionally carried out in the presence of from 0 to 10% by weight of at least one polymerisation regulator. (a) from 15 to 45% by weight of at least one ethylenically unsaturated monomer comprising at least one quaternary ammonium group; (b) from 5 to 80% by weight of at least one optionally substituted styrene; (c) from 0 to 50% by weight of at least one C 1-12 alkyl (meth) acrylate; (d) from 0 to 10% by weight of at least one ethylenically unsaturated monomer comprising an acid group; (e) from 0 to 10% by weight of at least one ethylenically unsaturated monomer comprising an amine group; and (f) from 0 to 20% by weight of at least one non-ionic ethylenically unsaturated monomer differing from (b), (c) and (e), the sum of (a) + (b) + (c) + (d) + (e) + (f) being 100% by weight, in a first emulsion polymerisation in the presence of at least one non-ionic emulsifier, and thereafter, in the aqueous liquid containing the cationic prepolymer, a second emulsion polymerisation is carried out, in the presence of at least one polymerisation initiator, of a monomer mixture comprising (i) from 10 to 70% by weight of at least one of an optionally substituted styrene or (meth) acrylonitrile; (ii) from 30 to 90% by weight of at least one C 1-18 alkyl (meth) acrylate; (iii) from 0 to 30% by weight of at least one vinyl ester of linear or branched C 1-30 carboxylic acids; and (iv) from 0 to 30% by weight of at least one non-ionic ethylenically unsaturated monomer differing from (i), (ii) and (iii), the sum of (i) + (ii) + (iii) + (iv) being 100% by weight, and the first emulsion polymerisation and/or the second emulsion polymerisation is optionally carried out in the presence of from 0 to 10% by weight of at least one polymerisation regulator. (i) from 10 to 70% by weight of at least one of an optionally substituted styrene or (meth) acrylonitrile; (ii) from 30 to 90% by weight of at least one C 1-18 alkyl (meth) acrylate; (iii) from 0 to 30% by weight of at least one vinyl ester of linear or branched C 1-30 carboxylic acids; and (iv) from 0 to 30% by weight of at least one non-ionic ethylenically unsaturated monomer differing from (i), (ii) and (iii), the sum of (i) + (ii) + (iii) + (iv) being 100% by weight, and the first emulsion polymerisation and/or the second emulsion polymerisation is optionally carried out in the presence of from 0 to 10% by weight of at least one polymerisation regulator.