The present invention relates to novel polymer dispersants in the form of comb polymers P and to a liquid composition containing solid fine particles, such as organic or inorganic pigments and fillers, and the polymer dispersants. The comb polymer P having at least 0.5 mol-%, e.g. 0.5 to 90 mol-%, based on the total amount of repeating units in the comb polymer, of repeating units A, selected from repeating units of the formulae la and lb: wherein R1 is selected from the group consisting of hydrogen, —S(═O)2Ra, C1-C20 alkyl, C3-C10 cycloalkyl, aryl, heteroaryl, aryl-C1-C4-alkyl and heteroaryl-C1-C4-alkyl; and X indicates a polymer group of the following formula X wherein Z indicates a polymer segment or a monovalent alkyl or alkenyl segment having from 10 to 100 carbon atoms; R1 is as defined above; k is 0, 1, 2, 3 or 4; n is 0, 1 or 2; A is a chemical bond or a divalent moiety selected from the group consisting of C1-C6 alkylene, —O—(C2-C6 alkylene) or —C(═O)—O—(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—; R2 is independently selected from the group consisting of —OH, —COOH, —COOCH3, —NH2, —NH(C1-C6 alkyl), —N(C1-C6 alkyl)2, —NO2, —S(═O)2Ra, C1-C20 alkyl, C1-C4 alkoxy, halogen, aryloxy, aryl, heteroaryl.