The charge transporting properties of a phosphorescent iridium(III) complex-cored dendrimer, with two dendrons attached to each ligand of the core are reported. The results show that the high photoluminescence quantum yield of this material is obtained without compromising charge transport. The hole mobility values are reported over a wide range of temperatures and electric fields using the charge-generation layer time-of-flight technique. The results are analysed using the Gaussian disorder model (GDM), the correlated disorder model, the polaronic correlated disorder model, and the short-range correlated Gaussian disorder model. It is found that the GDM model gives the most comprehensive description of hole transport in this material. In spite of its larger size, the hole mobility of the doubly dendronised material compares favourably with that of a smaller singly dendronised material, and its spherical shape leads to low energetic disorder and clearly non-dispersive charge transport. This shows how molecular shape can be used to combine favourable photoluminescence and charge-transporting properties.