While the strongly bound D-3h AH(3)(+) cations are favored energetically for CH3+ and SiH3+, C-s HA(+)... H-2 complexes are computed to be the global minima for A = Sn and Pb. The structures, relative energies, and dissociation limits (D-o) of the AH(3)(+) cations (A = C, Si, Ge, Sn, and Pb) were studied at the Becke3LYP density functional level [6-311++G(2d,2p) basis sets for C, Si, and Ge, (quasi)relativistic effective core potentials with TZ+2P valence basis sets for Sn and Pb]. The SiH3+ potential energy surface computed for calibration at the CCSD(T) lever is in very good quantitative agreement with the Becke3LYP results. The AH(3)(+)-->HA(+)... H-2 rearrangement illustrates the rare case where two transition states are connected directly (one high-lying, 45-58 kcal mol(-1) vs D-3h AH(3)(+) and one lower in energy, 0-37 kcal mol(-1)) without an intervening minimum. Due to the appreciable D-o values for both the AH(3)(+) and the HA(+)... H-2 species, they should be experimentally verifiable.