Pentaerythritol (PENT) was polycondensed with dimethyl sebacate (DMS) in bulk at 240 °C. With Ti(OBu)4 as the catalyst, an equimolar feed ratio resulted in gelation even when no vacuum was applied. When the PENT/DMS ratio was raised to 1.2/1.0, soluble viscous resins were obtained, but despite the excess of PENT, the conversion of methyl ester groups never exceeded 92%. With bismuth(III) n-hexanoate (BiHex3) as the catalyst and an 1.0/1.0 feed ratio, nonviscous polyesters were obtained with conversions <75%. When BiHex3 was used in the beginning and Ti(OBu)4 was added at a later stage, soluble viscous resins were obtained even at 1.0/1.0 feed ratio. Further polycondensations were conducted with higher PENT/DMS ratios. The reaction products were characterized by viscosity measurements, 1H NMR spectroscopy, and MALDI-TOF mass spectrometry. These measurements indicated the formation of hyperbranched polyesters almost free of cycles and ether groups. Furthermore, acylations with acetic or methacrylic anhydride were studied and quantitative conversions of the CH2OH groups were achieved.