Method for preparing a comb copolymer, the backbone of which is 2-acrylamido 2-methylpropane sulfonic acid, on which poly(N-alkyl acrylamide) or poly(N,N-dialkyl acrylamide) lateral segments are grafted, characterised in that it comprises the following sequence of steps: - a step (a) of reacting a compound of formula: CH 2 =C(R 2)-C(=O)-N(R 3)(R 4), in which R 2 represents a hydrogen atom or a methyl group, R 3 represents a hydrogen atom or a linear or branched alkyl radical comprising 1 to 4 carbon atoms and R 4, identical or different from R 3, represents a linear or branched alkyl radical comprising 1 to 4 carbon atoms, with a chain limiting compound of formula: Z-R 1 -NH 2, in which R 1 represents a divalent radical comprising 1 to 4 carbon atoms, and Z represents a functional group capable of acting as a transfer agent for radicals, in the presence of a polymerisation initiator, in a tert-butanol/water mixture, in order to obtain a poly(N-alkyl acrylamide) or poly(N,N-dialkyl acrylamide) telomer, of formula: H 2 N-R 1 -Z-{CH 2 -C(R 2)[C(=O)N(R 3)(R 4)]-} n -H in which n is an integer greater than or equal to 2 and less than or equal to 100, Z is a functional group capable of acting as a transfer agent of radicals, optionally - a step (b) of isolating and/or drying said telomer of formula obtained in step (a); - a step (c) of reacting, in the tert-butanol, the telomer of formula obtained in step (a), or optionally in step (b), with an acid chloride of formula: CH 2 =C(R 5)-C(=O)-Cl in which R 5 is a hydrogen atom or a methyl radical, and in a molar ratio / less than or equal to 10 and greater than or equal to 1, while maintaining the pH of the reaction medium at a value of between 8 and 10, in order to obtain a solution of the macromonomer of formula: CH 2 =C(R 5)-C(=O)NH-R 1 -Z-{CH 2 -C(R 2)[C(=O)N(R 3)(R 4)]-} n -H optionally - a step (d) of isolating and/or drying said macromonomer of formula obtained in step (c); - a step (e) of copolymerisation in tert-butanol of the macromonomer of formula coming from step (c) or step (d), with the ammonia salt of 2-acrylamido 2-methylpropane sulfonic acid and, if desired; - a step (f) of purifying the comb copolymer obtained in step (e). - a step (a) of reacting a compound of formula: CH 2 =C(R 2)-C(=O)-N(R 3)(R 4), in which R 2 represents a hydrogen atom or a methyl group, R 3 represents a hydrogen atom or a linear or branched alkyl radical comprising 1 to 4 carbon atoms and R 4, identical or different from R 3, represents a linear or branched alkyl radical comprising 1 to 4 carbon atoms, with a chain limiting compound of formula: Z-R 1 -NH 2, in which R 1 represents a divalent radical comprising 1 to 4 carbon atoms, and Z represents a functional group capable of acting as a transfer agent for radicals, in the presence of a polymerisation initiator, in a tert-butanol/water mixture, in order to obtain a poly(N-alkyl acrylamide) or poly(N,N-dialkyl acrylamide) telomer, of formula: H 2 N-R 1 -Z-{CH 2 -C(R 2)[C(=O)N(R 3)(R 4)]-} n -H in which n is an integer greater than or equal to 2 and less than or equal to 100, Z is a functional group capable of acting as a transfer agent of radicals, optionally - a step (b) of isolating and/or drying said telomer of formula obtained in step (a); - a step (c) of reacting, in the tert-butanol, the telomer of formula obtained in step (a), or optionally in step (b), with an acid chloride of formula: CH 2 =C(R 5)-C(=O)-Cl in which R 5 is a hydrogen atom or a methyl radical, and in a molar ratio / less than or equal to 10 and greater than or equal to 1, while maintaining the pH of the reaction medium at a value of between 8 and 10, in order to obtain a solution of the macromonomer of formula: CH 2 =C(R 5)-C(=O)NH-R 1 -Z-{CH 2 -C(R 2)[C(=O)N(R 3)(R 4)]-} n -H optionally - a step (d) of isolating and/or drying said macromonomer of formula obtained in step (c); - a step (e) of copolymerisation in tert-butanol of the macromonomer of formula coming from step (c) or step (d), with the ammonia salt of 2-acrylamido 2-methylpropane sulfonic acid and, if desired; - a step (f) of purifying the comb copolymer obtained in step (e).