The reactive oxirane groups were incorporated into the macromolecule as substituents in the side chains of loosely-grafted copolymer or in the arms of star-shaped copolymer using glycidyl methacrylate (GMA) in the controlled atom transfer radical polymerization (ATRP). The branched GMA copolymers with various architectures were obtained by using hydrophobic copolymers containing six and seven units of caprolactone 2-(methacryloyloxy)ethyl ester (CLMA) functionalized with bromoester groups, and trifunctional poly(ε-caprolactone) (PCL), as well as hydrophilic tri-, and six-functional acetal derivatives of D-glucopyranosides as (macro)initiators with biodegradable and biocompatible properties. The well-defined copolymers with core-shell structures and polymerization degrees of GMA in the range of 20–100 per side chain/arm at 20–70% of monomer conversion within 1–6 h and narrow molecular weight distributions (Mw/Mn = 1.14–1.4) were obtained. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers