The randomly branched poly(ethylene terephthalate) (BPET) was prepared by bulk polycondensation from dimethyl terephthalate (DMT) and ethylene glycol (EG), with 0.4-5.0 mol % (with respect to DMT) of glycerol (GL) as a branching agent. The glass transition and crystallization behavior was studied by differential scanning calorimetry (DSC). It was found that the glass transition temperature of BPET reduced with the increasing content of GL until 1.2 mol %, and then increases a little at high degrees of branching. When compared with a linear PET, the crystallization temperature of BPET from the melt shifted to higher temperature as GL content was smaller than 1.2 mol %, and then became lower while GL load was added. Nonisothermal crystallization kinetics was studied through the modified Avrami analysis. It was revealed that the overall crystallization rate parameter of BPET became larger when the GL content was less than 1.2 mol %, then turned to lower at higher branching degree. This indicated that low degree of branching could enhance the overall crystallization of poly(ethylene terephthalate) (PET), whereas high degree of branching in the range of 3.5-5.0 mol % would block the development of crystallization. On the basis of Hoffman's secondary crystallization theory, the product sigma sigma(e) of the free energy of formation per unit area of the lateral and folding surface was calculated. According to the change of the product sigma sigma(e) with the degree of branching, a possible explanation was presented to illuminate this diverse effect of different degrees of branching on crystallization. (C) 2008 Wiley Periodicals, Inc.