A series of AB(2)-R monomers that were composed of one alkynyl group (A), two azido groups (B-2), and a dangling group (R) were applied in the copper-catalyzed azide alkyne cycloaddition (CuAAC) polymerization for synthesis of hyper branched polymers. Several structural variables, including the linker between the alkynyl group and the diazido unit (S1), the linker between the two azido groups (S2), and the composition of R group, were systematically changed to study their effects on the polymerization kinetics, the molecular weights, and the degree of branching (DB) of the hyperbranched polymers. Within the investigation, all polymerizations eventually showed chain-growth features although their starting moments when exhibiting linear increase of molecular weights based on conversions were delayed by the increased length of Si linker, but little influenced by S2 and R groups. The AB(2)-R monomer with longer S1 linker, due to slower hopping of Cu catalysts between neighboring structural units, resulted in more leftover oligomers and decreased overall molecular weights. High DB > 0.75 was achieved in all hyperbranched polymers with various Si lengths and R groups and slightly influenced by the steric hindrance and the rate of catalyst hopping. Instead, the increase of S2 linker from C2 to C4 lowered the reactivity of the second azido group in linear units and resulted in an evident decrease of the DB from DB = 0.73 to 0.55, respectively.