Total absorption cross-sections and product rotational quantum state distributions are computed from first principles for the first two ultraviolet absorption bands of the HOBr molecule corresponding to excitation to the 11A″ and 21A′ states. The dynamical calculations are based on ab initio potential energy surfaces and transition dipole moment surfaces. The theory of triatomic photodissociation is presented in detail, in a manner which is clearer than previously available, and an important correction is made to the theoretical formulae. The theory takes proper account of angular momentum coupling and of the parity of all of the constituent wavefunctions. It is applicable to any initial (or final) angular momentum. The computed absorption bands agree reasonably well with available experimental results but highlight shortcomings of the electronic structure calculations on which these dynamical calculations are based. Predictions are made for the effect of excitation of initial vibrational states on the absorption line shapes.