Use of high functionality hyperbranched polycarbonates obtainable by a) preparing one or more different condensation products (K) either by a1) reacting at least one organic carbonate (A) of the general formula RO[(CO)O].sub.nR with at least one aliphatic, aliphatic/aromatic or aromatic alcohol (B) having at least 3 OH groups by elimination of alcohols ROH, where each R is independently a straight chain or branched aliphatic, aromatic-aliphatic or aromatic hydrocarbyl radical having 1 to 20 carbon atoms and the R radicals may also be bonded to each other to form a ring comprising the grouping --O[(CO)O].sub.n--, where n is an integer from 1 to 5, or a2) reacting phosgene, diphosgene or triphosgene with the aliphatic, aliphatic/aromatic or aromatic alcohol (B) to liberate hydrogen chloride, the quantitative ratio of the alcohols (B) to the carbonates (A) or to the phosgenes in the reaction mixture being so chosen that the condensation products (K) comprise on average either one carbonate or carbamoyl chloride group and more than one OH group or one OH group and more than one carbonate or carbamoyl chloride group, and b) intermolecularly reacting the condensation products (K) from step a), as a dispersant for a pigment.