Triple ionization of molecular systems is investigated theoretically by means of the three-particle propagator. This enables us to efficiently calculate the very dense triple ionization spectra. To be able to interpret these spectra an atomic three-hole population analysis is developed which provides information about the charge distribution in the molecular trication. In exemplary applications on CO and a series of fluorides the use of the approach is demonstrated. A large number of triply ionized electronic states are energetically accessible in the available particle impact ionization experiments and it is shown that many of these states contribute to the observations. Triply ionized states are also produced by Auger decay. In particular, shake-off satellite lines of molecular Auger spectra can be reproduced using the triple ionization energies from the propagator calculation and an estimate of the transition rates based on the three-hole population analysis. In general a dramatically growing complexity of the triple ionization spectra with increasing molecular size is demonstrated. In spite of this complexity the three-hole population analysis is of valuable help for the interpretation of the spectra and often a simple picture in terms of various hole-localization patterns arises.