Multiarm stars containing a hyperbranched poly(ethyleneimine) core of different molecular weight and poly(lactide) arms were synthesized by cationic ring-opening polymerization of lactide from a hyperbranched poly(ethyleneimine) core. After characterization by rheometry, calorimetry, thermogravimetry and nuclear magnetic resonance, these polymers were used as chemically modifiers in the anionic curing of diglycidylether of bisphenol A epoxy resin. The curing process was studied by dynamic scanning calorimetry, demonstrating the influence of the mobility of the reactive species and the hydroxyl content on the curing kinetics. The resulting materials were characterized by thermal and mechanical tests. The addition of the multiarm stars led to homogeneous materials with a slight improvement on the impact strength in comparison with the neat material, without compromising the glass transition temperature. The reworkable nature of the materials was demonstrated by monitoring the changes in their glass transition under thermal rework conditions.