Mixtures of conjugates in which each conjugate in the mixture comprises a growth hormone drug coupled to an oligomer that includes a polyalkylene glycol moiety wherein the mixtures have a molecular weight distribution with a standard deviation of less than about 22 Daltons are disclosed. Methods of treating growth hormone deficiency in a subject in need of such treatment and methods of accelerating the growth rate of an animal arc also disclosed. Processes for synthesizing substantially monodispersed mixtures of conjugates wherein each conjugate comprises a growth hormone drug coupled to an oligomer that comprises a polyethylene glycol moiety are further provided.