Low molar mass hyperbranched polyesters were prepared by polycondensation of 1,1,1-tris(hydroxymethyl)ethane and various dimethyl esters of aliphatic dicarboxylic acids in bulk. The usefulness of nontoxic bismuth salts as transesterification catalysts for these polycondensations was studied. The maximum conversion increased, and the reaction time decreased in the following sequence of increasing reactivity: dimethyl sebacate < adipate < glutarate < succinate. Regardless of the monomer combination, gelation occurred at conversions > 91.5%. The hyperbranched structure was proven by H-1 NMR spectroscopy and the absence of cyclic elements by MALDI-TOF mass spectrometry. Quantitative acylation of all CH2OH groups was achieved with an excess of acetic anhydride or methycrylic anhydride. (c) 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 231-238, 2009