The present paper deals with electronic excitation transfer in columnar liquid crystals formed by disklike molecules. The transport process is considered to occur in the singlet state via random walk hopping and is studied by Monte Carlo simulations. The distance dependence of the hopping probability is determined by the extended dipole approximation. Long-range steps, both intracolumnar and intercolumnar, are taken into account. The influence of (i) the number of nearest neighbors to which hops may occur, (ii) the intercolumnar distance, (iii) the length and the orientation of the transition dipoles, on the root mean square displacement along the column axis and the survival probability in presence of traps is investigated. It is shown that long-range hops slow down the transfer process, The transport is initially one-dimensional and becomes three-dimensional at longer times. The crossover regime is shifted to shorter times when the intercolumnar distance decreases or the length of the transition dipoles increases. The motion of the excitation is accelerated either by a better ordering of the transition dipoles around the column axis or by a continuous change of their orientation during the walk.