We present dynamical studies of the dissociation of polycyclic aromatic hydrocarbon (PAH) radical cations in their ground electronic states with significant internal energy. Molecular dynamics simulations are performed, the electronic structure being described on-the-fly at the self-consistent-charge density functional-based tight binding (SCC-DFTB) level of theory. The SCC-DFTB approach is first benchmarked against DFT results. Extensive simulations are achieved for naphthalene [Formula: see text], pyrene [Formula: see text] and coronene [Formula: see text] at several energies. Such studies enable one to derive significant trends on branching ratios, kinetics, structures and hints on the formation mechanism of the ejected neutral fragments. In particular, dependence of branching ratios on PAH size and energy were retrieved. The losses of H and H (recognized as the ethyne molecule) were identified as major dissociation channels. The H/CH ratio was found to increase with PAH size and to decrease with energy. For [Formula: see text], which is the most interesting PAH from the astrophysical point of view, the loss of H was found as the quasi-only channel for an internal energy of 30 eV. Overall, in line with experimental trends, decreasing the internal energy or increasing the PAH size will favour the hydrogen loss channels with respect to carbonaceous fragments.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.