We present a density functional theory (DFT) study on charge-transport related properties in a series of discotic systems based on 1,3,5-triazine and tris(1,2,4)triazolo(1,3,5)triazine central cores as electron acceptor units, and phenyl-thiophene and N-carbazolyl-thiophene segments as electron donating units. The presence of both electron donor and acceptor moieties in the π-conjugated core could lead to new discotic liquid crystals (DLC) materials which are predicted to display ambipolar charge transport behavior in such a way that electrons could move through the central part of the next cores while holes mainly do through the peripheral groups. A significant increase in hole mobility when N-carbazolyl is present as electron donor unit in the peripheral region is predicted. In addition, a detailed topological analysis of the electron charge density within the framework provided by Quantum Theory of Atoms in Molecules (QTAIM) has been performed in order to characterize intra and intermolecular interactions in terms of hydrogen bonds and/or π…π stacking which contribute to the stabilization of the columnar stack and the helical self-assembly at molecular scale.