This paper explores how charge carrier mobilities in columnar discotic liquid crystals may be enhanced. The hole mobility and its temperature dependence has been measured in a variety of triphenylene based DLCs using the time of flight method in the mesophase and where possible in the glassy (or crystalline) phase. A model using the Holstein small polaron is fitted to the results and the resulting polaron self energy and bandwidth are found. Where trapping is observed it shows a tendency to trap at a faster rate as electric field is increased. This is discussed in terms of dimensionality of the carrier transport. Some transient data is fitted to the Noolandi multiple trapping model and trapping rates and detrapping rates using that model are recovered. Their variation with electric field is discussed.