We show that glycosaminoglycans (GAGs) with high molecular weight can be grafted via their reducing end on hyper-branched synthetic cores by oxime condensation without the need of any previous functionalisation of the polysaccharide. The versatility of this reaction is demonstrated by the use of hyaluronan, chondroitin sulfate and heparin with up to 60 sugar units. The isothermal calorimetry analysis demonstrated that the generated star-like glycopolymers have superior bioactivity. Moreover, when mixed with positively charged proteins (e.g. FGF-2) they form microfiber structures instead of the spherical nanocomplexes described for linear GAGs. Our results suggest that the described star-like GAG are closer mimics of the proteoglycans at structural and functional level and therefore have a huge potential in the development of tissue engineering platforms and therapeutics by modulating the activity and presentation of various proteins such as growth factors.