The present paper deals with the photophysical properties of columnar Liquid crystals formed by hexakis-(alkyloxy)triphenylenes. Absorption and fluorescence spectra of solutions are analyzed on the basis of quantum chemical calculations performed by the CS-INDO-CI (conformations spectra-intermediate neglect of differential overlap-configuration interaction) method : the absorption maximum is due to the S-0-->S-4 transition while fluorescence originates from the weak S-0-->S-1 transition. In columnar aggregates, the former transition corresponds to delocalized excited states while the latter corresponds to localized ones; calculation of intermolecular interactions shows that, at the temperature domain of the mesophases, all the molecules have the same excitation energy and, therefore, no spectral diffusion of the fluorescence is expected, in agreement with the time-resolved emission spectra. Excitation transfer is investigated by studying the fluorescence decays of mesophases doped with energy traps. Their analysis is made by means of Monte Carlo simulations considering both intracolumnar and intercolumnar jumps and using four different models for the distance dependence of the hopping probability. The best description is obtained with a model based on the extended dipole approximation and taking into account molecular orientation.