Hyperbranched poly(ethyleneimine) (PEI) has been modified by the addition of propargyl acrylate following a Michael addition reaction. On this polymer (PEI-yne) a copper (I)-catalyzed azide alkyne cycloaddition (CuAAC) has been performed to obtain a multifunctional triazole initiator (PEI-TA). After structural and thermal characterization, this polymer has been used in different proportions as anionic multifunctional macroinitiator in diglycidyl ether of bisphenol A (DGEBA) homopolymerization. The curing process has been studied by calorimetry and the thermosets obtained have been thermally characterized and compared with thermosets prepared by using 1-methylimidazole (1-MI) as standard initiator. The electron microscopy inspection of the fracture surfaces of the new materials prepared shows the formation of submicrometer particles that should enhance toughness characteristics, changing smooth fracture surfaces in 1-MI initiated materials to multi-planar surface with tortuous and thicker cracks.