The present invention relates to methodology for polymer grafting by a polysaccharide synthase and, more particularly, polymer grafting using the hyaluronate or chondroitin or heparin/heparosan synthases from Pasteurella, in order to create a variety of glycosaminoglycan oligosaccharides having a natural or chimeric or hybrid sugar structure with a targeted size that are substantially monodisperse in size. The present invention also relates to methodology for polymer grafting by a polysaccharide synthase to form glycosaminoglycan polymers having an unnatural structure.