The present invention relates to conjugates of biologically active compounds, preferably therapeutically active compounds, with polymeric moieties having low polydispersity, as well as controlled polymerisation processes for producing the conjugates. An initiation for a controlled radical polymerisation process comprises a biologically active, usually therapeutically active, moiety and the monomer includes zwitterionic monomer for instance 2-methacryloyloxyethyl-2′-trimethylammonium ethyl phosphate inner salt. The process allows close control of the molecular weight and polydispersity of the polymeric moiety and the possibility of optimizing the delivery characteristics of the active agent.