In this work, we address the formation of polarons in hyperbranched polymers and their conduction properties from a theoretical and numerical perspective. As a chemical realization, we consider condensed triarylamine molecules. The topology of the macromolecules follows the concept of regular hyperbranched fractals. The electronic structure is described by a pi orbital tight-binding Hamiltonian extended by a reaction field, which takes dielectric polarization effects into account. Excess charges are predominantly localized at the nitrogen atoms; the trapping energies and the hopping rates depend on the local environment of the monomers via their coordination numbers. For systems containing up to 64 monomers, the structures studied here provide fast charge transport along the backbone of the polymer, whereas the side chains are rapidly depopulated. We therefore suggest the use of hyperbranched triarylamines as bridging elements to enhance the mobility of holes in conducting polymers.