Controlled radical polymerization of vinyl monomers with multivinyl cross-linkers leads to the synthesis of highly branched polymers with controlled spatial density of functional chain ends. The resulting polymers synthesized in this manner have large dispersities resulting from a mixture of unreacted primary chains, low molecular weight branched species, and high molecular weight highly branched species. Through the use of fractional precipitation, we present a synthetic route to high molecular weight highly branched polymers that are absent of low molecular weight species and that contain reactivity toward amines for controlled postpolymerization modification. The controlled spatial density of functional moieties on these high molecular weight macromolecular constructs enable new functional biomaterials with the potential for application in regenerative medicine, immunoengineering, imaging, and controlled drug delivery.