A copolymer which comprises, in copolymerized form, (A) 60 to 99% by weight of at least one monoethylenically unsaturated polyalkylene oxide monomer of the formula I (I) in which the variables have the following meanings: X is —CH2— or —CO—, if Y is —O—; is —CO—, if Y is —NH—; Y is —O— or —NH—; R1 is hydrogen or methyl; R2 are identical or different C2-C6-alkylene radicals, which may be arranged blockwise or randomly; R3 is hydrogen or C1-C4-alkyl; n is an integer from 25 to 75, (B) 1 to 40% by weight of at least one quaternized nitrogen-containing monoethylenically unsaturated monomer selected from the group consisting of monomers of formula Ha to IId (Ha-IId) in which the variables have the following meanings: R is C1-C4-alkyl or benzyl; R′ is hydrogen or methyl; Y is —O— or —NH—; A is C1-C6-alkylene; X— is halide, C1-C4-alkyl sulfate, C1-C4-alkylsulfonate and Ci-C4-alkyl carbonate, (C) 0 to 10% by weight of anionic monoethylenically unsaturated monomers, and (D) 0 to 30% by weight of other nonionic monoethylenically unsaturated monomers and has an average molecular weight Mw of >100,000.