Carrier transits and photoconductivity in hexaalkoxytriphenylene- (HAT) based liquid crystals and their binary 1:1 mixtures with hexaalkylphenyltriphenylene (PTP) are analyzed using time-dependent diffusion theory. The HAT6 derivatives, which show the best transits, can be modeled with a homogeneously distributed single-trap model. The transit data for the compound formed by the 1:1 binary mixture of HAT11-PTP9, which exhibits better columnar stability and higher carrier mobility, cannot, however, be explained using homogeneous multiple trapping models alone. The evidence presented in this paper also suggests that the trap-limited carrier relaxation does indeed obey the law of one-dimensional transport, which says that with an electric field. i.e., in the drift-limited regime, carriers take less time to reach the equilibrium values of the diffusivity. This is a particularly exciting result, which directly confirms rigorous theoretical predictions and is consistent with the previously discussed data taken in the crystalline phase of HAT6.