Compared with linear polymers, more factors may affect the glass-transition temperature (T-g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T-g's decrease with increasing content of end-group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end-group free volumes are often a prevailing factor according to the literature. In this work, chain-end, free-volume theory was extended for predicting the relations of T-g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one-pot approaches of either polycondensation or self-condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T-g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T-g values decreased with increasing molecular weight in the low-molecular-weight range; however, they increased with increasing molecular weight in the high-molecular-weight range. T-g values decreased with increasing log M and then turned to a constant value in the high-molecular-weight range. The plot of T-g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight-line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain-end, free-volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end-group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T-g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. (C) 2004 Wiley Periodicals, Inc.