Process for producing end-group-functionalized oligomers based on acrylic monomers by means of free-radical polymerization, initiated by at least one initiator, starting from an amount of monomer of 80 to 95 mol% of at least one monomer A, selected from the group consisting of acrylates of the general formula CH 2 =CH(COOR I), methacrylates of the general formula CH 2 =C(CH 3)(COOR I), acrylamides of the general formula CH 2 =CH(CONR II R III) and methacrylamides of the general formula CH 2 =C(CH 3)(CONR II R III), wherein R I is an alkyl residue having one to 26 carbon atoms and R II and R III are each alkyl residues having one to 26 carbon atoms or hydrogen, and 5 to 20 mol% of at least one monomer B, selected from the group consisting of styrene, o-methylstyrene, m-methylstyrene, p-methylstyrene, 4-tert-butylstyrene, 2,4,6-trimethylstyrene, 4-vinylanisole, 4-trifluoromethylstyrene, 4-vinylbiphenyl, 2-vinylnaphthalene and 9-vinylanthracene, wherein - the sum total of the amounts of monomers A and monomers B is 100 mol%, - the polymerization is controlled by means of a difunctional regulator comprising the functional groups R F1 and R F2, where the group R F1 is an unsubstituted sulfanyl group and where the group R F2 of the regulator is selected from the list consisting of hydroxyl groups (-OH), carboxyl groups (-COOH), protected primary amino groups (-NH 2), protected secondary amines (-NHR), characterized in that - the initiator is an azo or peroxo initiator, which is selected such that it does not bear any R F1 and R F2 functional groups, - the total amount of monomer, the initiator and the regulator are initially charged, - wherein the amount of regulator is selected such that the quantitative ratio of (total used) monomers to (total used) regulator molecules is from 100: 20 to 100: 0.5, - the polymerization is conducted until monomer conversion reaches at least 96%, - the residual amount of regulator is less than 5 mol%, - and in a subsequent process step the macromolecules thus obtained are reacted, in the same reactor in which the polymerization was carried out, with at least one compound Z having a functional group R F3 and an ethylenic double bond, - wherein at least that part of the compound Z comprising the ethylenic double bond is linked to the macromolecule by reaction of the functional group R F2 with the functional group R F3. 80 to 95 mol% of at least one monomer A, selected from the group consisting of acrylates of the general formula CH 2 =CH(COOR I), methacrylates of the general formula CH 2 =C(CH 3)(COOR I), acrylamides of the general formula CH 2 =CH(CONR II R III) and methacrylamides of the general formula CH 2 =C(CH 3)(CONR II R III), wherein R I is an alkyl residue having one to 26 carbon atoms and R II and R III are each alkyl residues having one to 26 carbon atoms or hydrogen, and 5 to 20 mol% of at least one monomer B, selected from the group consisting of styrene, o-methylstyrene, m-methylstyrene, p-methylstyrene, 4-tert-butylstyrene, 2,4,6-trimethylstyrene, 4-vinylanisole, 4-trifluoromethylstyrene, 4-vinylbiphenyl, 2-vinylnaphthalene and 9-vinylanthracene, - the sum total of the amounts of monomers A and monomers B is 100 mol%, - the polymerization is controlled by means of a difunctional regulator comprising the functional groups R F1 and R F2, where the group R F1 is an unsubstituted sulfanyl group and where the group R F2 of the regulator is selected from the list consisting of hydroxyl groups (-OH), carboxyl groups (-COOH), protected primary amino groups (-NH 2), protected secondary amines (-NHR), - the initiator is an azo or peroxo initiator, which is selected such that it does not bear any R F1 and R F2 functional groups, - the total amount of monomer, the initiator and the regulator are initially charged, - wherein the amount of regulator is selected such that the quantitative ratio of (total used) monomers to (total used) regulator molecules is from 100: 20 to 100: 0.5, - the polymerization is conducted until monomer conversion reaches at least 96%, - the residual amount of regulator is less than 5 mol%, - and in a subsequent process step the macromolecules thus obtained are reacted, in the same reactor in which the polymerization was carried out, with at least one compound Z having a functional group R F3 and an ethylenic double bond, - wherein at least that part of the compound Z comprising the ethylenic double bond is linked to the macromolecule by reaction of the functional group R F2 with the functional group R F3.