The use of a polymer P having at least one functional group of the formula I: bound to one of the termini and/or to the backbone of the polymer, where # indicates the point of attachment to the terminus and/or to the polymer backbone; k is 0, 1, 2, 3 or 4; m is 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9; A is a chemical bond or a divalent moiety selected from the group consisting of C 1 -C 6 alkylene, -O-(C 2 -C 6 alkylene), -C(=O)-O-(C 2 -C 6 alkylene), -NR 3 -(C 2 -C 6 alkylene) and C(=O)-NR 3 -(C 2 -C 6 alkylene), where the C 2 -C 6 alkylene part is attached to Q; Q is a divalent moiety selected from the group consisting of -O-, -NH- and -S-; R 1 is independently selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 20 alkyl, C 1 -C 4 alkoxy, halogen, aryloxy, aryl, heteroaryl, where aryl, hetaryl and aryloxy are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen; R 2 is selected from the group consisting of hydrogen, -S(=O) 2 R 4, C 1 -C 20 alkyl, C 3 -C 10 cycloalkyl, aryl, heteroaryl, aryl-C 1 -C 4 -alkyl and heteroaryl-C 1 -C 4 -alkyl, where aryl and hetaryl in the four last mentioned radicals are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen; R 3 is selected from the group consisting of hydrogen, -S(=O) 2 R 4, C 1 -C 20 alkyl, C 3 -C 10 cycloalkyl, aryl and heteroaryl, where aryl and hetaryl are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen; R 4 is selected from the group consisting of OH, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, C 1 -C 4 alkyl, C 1 -C 4 alkoxy, aryl and heteroaryl, where aryl and hetaryl are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen; where the polymer P is selected from the group consisting of aliphatic polyesters, poly-(C 2 -C 4 -alkylene oxide)s, aliphatic polyetheresters, aliphatic polycarbonates and polymers, which have a C-C backbone comprising repeating units M1, selected from polymerized C 1 -C 10 -alkyl (meth)acrylates, polymerized C 1 -C 10 -alkyl-(poly-C 2 -C 4 -alkyleneglycol) (meth)acrylates and polymerized vinylaromatic hydrocarbon compounds, as a dispersant for pigment and fillers. # indicates the point of attachment to the terminus and/or to the polymer backbone; k is 0, 1, 2, 3 or 4; m is 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9; A is a chemical bond or a divalent moiety selected from the group consisting of C 1 -C 6 alkylene, -O-(C 2 -C 6 alkylene), -C(=O)-O-(C 2 -C 6 alkylene), -NR 3 -(C 2 -C 6 alkylene) and C(=O)-NR 3 -(C 2 -C 6 alkylene), where the C 2 -C 6 alkylene part is attached to Q; Q is a divalent moiety selected from the group consisting of -O-, -NH- and -S-; R 1 is independently selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 20 alkyl, C 1 -C 4 alkoxy, halogen, aryloxy, aryl, heteroaryl, where aryl, hetaryl and aryloxy are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen; R 2 is selected from the group consisting of hydrogen, -S(=O) 2 R 4, C 1 -C 20 alkyl, C 3 -C 10 cycloalkyl, aryl, heteroaryl, aryl-C 1 -C 4 -alkyl and heteroaryl-C 1 -C 4 -alkyl, where aryl and hetaryl in the four last mentioned radicals are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen; R 3 is selected from the group consisting of hydrogen, -S(=O) 2 R 4, C 1 -C 20 alkyl, C 3 -C 10 cycloalkyl, aryl and heteroaryl, where aryl and hetaryl are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of -OH, -COOH, -COOCH 3, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, -NO 2, -S(=O) 2 R 4, C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen; R 4 is selected from the group consisting of OH, -NH 2, -NH(C 1 -C 6 alkyl), -N(C 1 -C 6 alkyl) 2, C 1 -C 4 alkyl, C 1 -C 4 alkoxy, aryl and heteroaryl, where aryl and hetaryl are unsubstituted or substituted by 1, 2, 3 or 4 radicals selected from the group consisting of C 1 -C 4 alkyl, C 1 -C 4 alkoxy and halogen;