Hyperbranched polymers with a degree of branching of 100% were prepared by catalyst transfer Suzuki-Miyaura polymerization of AB(2) monomers carrying one boronic acid and two aromatic bromo functional groups; in contrast, Suzuki-Miyaura polymerization of the same AB(2) monomers using a traditional catalyst afforded hyperbranched polymers with a branching degree of only similar to 56%. This is a nice example of controlling the topology of hyperbranched polymers via the catalyst.