The photochemistry of the water molecule has revealed a wealth of quantum phenomena, which arise from the involvement of several coupled electronic states with very different potential energy surfaces. Most recently, dissociation from single rotational levels of its C̃(1)B1 state near 124 nm has been attributed to a vibronically coupled decay via the lower Ã-state surface, despite a large vertical energy gap of 2.8 eV. Similar conclusions have been reached for subsequent experimental data for D2O. The present paper presents further experimental data for HOD and for both the H+OD(X) and D+OH(X) products. Unlike the cases for H2O and D2O, the vibrational populations for hydroxyl products do not follow a smooth distribution with v(OH∕OD). In particular, for OH there is a clear alternation in population for all the strong peaks, with odd v favoured over even v. These experimental data are analysed using new MRCI+Q calculations, which have been used to generate potential surfaces and associated non-adiabatic matrix elements for transition from the adiabatic C̃-state to lower unbound potential surfaces; and hence, to guide dynamical calculations using time-dependent wavepackets. It is concluded that although there is a minor contribution from the C̃→ Ã decay route, the major route follows C̃→ (1)A2 → Ã. This is mediated through two regions of near degeneracy of the elusive (1)A2 surface with C̃ for short bonds ca. 0.8 Å; and between (1)A2 and Ã with long bonds ≥2 Å, thereby bridging the vertical energy gap. The striking population alternation for the D+OH(X) products is attributed to dynamic symmetry breaking on the (1)A2 surface.