The present invention relates to novel polymer dispersants and to a liquid compositions containing solid fine particles, such as organic or inorganic pigments and fillers, and the polymer dispersants. The polymer dispersants have at least one functional moiety of the formula I, which is bound to one of the termini or to the backbone of the polymer: (I) 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 C1-C6 alkylene, —O—(C2-C6 alkylene), —C(═O)—O—(C2-C6 alkylene), —NR3—(C2-C6 alkylene) and C(═O)—NR3—(C2-C6 alkylene), where the C2-C6 alkylene part is attached to Q; Q is a divalent moiety selected from the group consisting of —O—, —NH— and —S—; R1 is independently selected from the group consisting of —OH, —COOH, —COOCH3, —NH2, —NH(C1-C6 alkyl), —N(C1-C6 alkyl)2, —NO2, —S(═O)2R4, C1-C20 alkyl, C1-C4 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, —COOCH3, —NH2, —NH(C1-C6 alkyl), —N(C1-C6 alkyl)2, —NO2, —S(═O)2R4, C1-C4 alkyl, C1-C4 alkoxy and halogen; R2 is selected from the group consisting of hydrogen, —S(═O)2R4, C1-C20 alkyl, C3-C10 cycloalkyl, aryl, heteroaryl, aryl-C1-C4-alkyl and heteroaryl-C1-C4-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, —COOCH3, —NH2, —NH(C1-C6 alkyl), —N(C1-C6 alkyl)2, —NO2, —S(═O)2R4, C1-C4 alkyl, C1-C4 alkoxy and halogen; R3 is selected from the group consisting of hydrogen, —S(═O)2R4, C1-C20 alkyl, C3-C10 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, —COOCH3, —NH2, —NH(C1-C6 alkyl), —N(C1-C6 alkyl)2, —NO2, —S(═O)2R4, C1-C4 alkyl, C1-C4 alkoxy and halogen; R4 is selected from the group consisting of OH, —NH2, —NH(C1-C6 alkyl), —N(C1-C6 alkyl)2, C1-C4 alkyl, C1-C4 alkoxy, aryl and heteroaryl,