Hyperbranched copolymers with segmented structures were synthesized using a chain-growth copper catalyzed azide alkyne cycloaddition (CuAAC) polymerization via sequential monomer addition in one pot. Three AB(2)-type monomers that contained one alkynyl group (A), two azido groups (B), and one dangling group, either benzyl or oligo(ethylene oxide) (EOx, x = 3 and 7.5), were used in these CuAAC reactions. Varying the addition sequences and feed ratios of the monomers produced a variety of hyper branched copolymers with tunable compositions, molecular weights, segmented structures, and consequently glass transition temperature (T-g). It was found that the T-g of hyperbranched copolymers was little affected by the polymer molecular weights when M-n >= 5000. However, the values of T-g were significantly determined by the compositions of the terminal groups and the outermost segment of the hyperbranched copolymers. The last added AB(2) monomer in the polymerization formed an outermost "shell" and shielded the contribution of inner segments to the glass transition of the copolymers, reflecting a chain sequence effect of hyperbranched polymers on the thermal properties.