Design, controlled synthesis, physico-chemical and biological characteristics of novel well-defined biodegradable star-shaped copolymers intended for advanced drug delivery is described. These new biocompatible star copolymers were synthesised by grafting monodispersed semitelechelic linear (sL) N-(2-hydroxypropyl)methacrylamide copolymers onto a 2,2-bis(hydroxymethyl)propionic acid (bisMPA)-based polyester dendritic core of various structures. The hydrodynamic diameter of the star copolymer biomaterials can be tuned from 13 to 31 nm and could be adjusted to a given purpose by proper selection of the bisMPA dendritic core type and generation and by considering the sL copolymer molecular weight and polymer-to-core molar ratio. The hydrolytic degradation was proved for both the star copolymers containing either dendron or dendrimer core, showing the spontaneous hydrolysis in duration of few weeks. Finally, it was shown that the therapy with the biodegradable star conjugate with attached doxorubicin strongly suppresses the tumour growth in mice and is fully curative in most of the treated animals at dose corresponding approximately to one fourth of maximum tolerated dose (MTD) value. Both new biodegradable systems show superior efficacy and tumour accumulation over the first generation of star copolymers containing non-degradable PAMAM core.