The present invention provides branched water-soluble polymers that allow two or more water-soluble polymers to be conjugated to another species. The branched polymers provide access to therapeutic agents that are conjugated at a single site to two or more water-soluble polymers. The branched polymers are based upon branch points that are simple branched alkyl structures, reactive side-chain amino acids and small peptides of reactive side-chain amino acids, and saccharides. Also provided is a method for preparing mono-disperse poly(ethylene glycol) of a well-defined and determinable molecular weight, and a method for the rational end-functionalization of poly(ethylene glycol). Conjugates of the branched water-soluble polymers with diverse species, e.g., peptides, lipids, glycolipids and small molecules are also provided.