¹H NMR and ¹³C NMR spectrometry (1-dimensional and 2-dimensional) have been used to assign chemical resonances and determine the degrees of branching for polyesters synthesized by the Lewis acid (dibutyltin(IV)oxide)-catalyzed polycondensation of glycerol with either succinic acid (n (aliphatic chain length) = 2), glutaric acid (n = 3) or azelaic acid (n = 7) in quasi-melt solutions with toluene. When 1:1 and 2:1 (diacid:glycerol) molar ratios were used, it was found that the glutaric acid-derived polymers gave the highest degree of polymer branching (31.2%, 85.6%, respectively) after the 24 h reaction period followed by the succinic acid-derived polymers (39.4%, 41.9%, respectively) and the azelaic acid-derived polymers (9.9%, 13.9%, respectively). Reactions performed at reflux for 24 h resulted in a 70.8% and 56.7% decrease in degree of branching for succinic acid and glutaric acid-derived polyesters, respectively. There is no indication that degree of branching is significantly affected by the presence or absence of solvent according to the results obtained in this research.