An A2 + B3 polymerization for the synthesis of hyperbranched polymers was altered using oligomeric precursors in place of either one or both of the monomer pairs to synthesize highly branched macromolecules. Unique topologies that are intermediates between long-chain branched and hyperbranched structures were obtained and the term "highly branched" was used to define these novel architectures. Various types of highly branched polymers, such as polyurethanes, poly(urethane urea)s, poly(ether ester)s, and poly(arylene ether)s were synthesized using the oligomeric A2 + B3 strategy. The molar mass of the oligomeric precursor permitted the control of the molar mass between branch points, which led to interesting macromolecular properties, such as superior mechanical performance to conventional hyperbranched polymers, disrupted crystallinity, improved processibility, and a multitude of functional end groups. Highly branched poly(urethane urea)s and polyurethanes exhibited microphase-separated morphologies as denoted by dynamic mechanical analysis. The similarity in soft segment glass transition behavior and mechanical properties of the branched systems with that of the linear analogues suggested these materials have considerable promise for a variety of applications. When a polycaprolactone triol was utilized as the B3 oligomer for the synthesis of highly branched polyurethane elastomers, the high degree of branching resulted in a completely amorphous soft segment, whereas the linear analogue with equivalent soft segment molar mass retained the crystallinity of polycaprolactone segment. Oligomeric A2 + B3 methodology was further utilized to tailor the degree of branching of poly(ether ester)s that were developed based on slow addition of dilute solution of poly(ethylene glycol) (PEG) (A2) to a dilute solution of 1,3,5-benzenetricarbonyl trichloride (B3) at room temperature in the presence of triethylamine. A revised definition of the degree of branching was proposed to accurately describe the branched poly(ether ester)s and the degree of branching decreased as the molar mass of the PEG diols was increased. Moreover, branched poly(arylene ether)s were prepared via a similar oligomeric A2 + B3 polymerization of phenol endcapped telechelic poly(arylene ether sulfone) oligomers (A2) and tris(4-fluorophenyl) phosphine oxide (B3) in solution. Highly branched poly(ether ester)s were also synthesized in the melt phase using the oligomeric A2 + B3 polymerization strategy. Melt polymerization effectively limited the cyclization reactions, which are common in A2 + B3 polymerizations in solution, and overcame the need for large amounts of polymerization solvent typical of A2 + B3 systems. Finally, a new family of telechelic polyester ionomers was synthesized based on phosphonium bromide salt end groups and branching allowed the incorporation of higher levels of ionic end groups compared to linear analogues. / Ph. D.