The quantum dynamics of photoassociative collisions O(³P)+H(²S) controlled by picosecond laser pulses is explored in the ground (X ²Π) and excited (A ²Σ⁺) electronic states. Coupled Schrödinger equations are solved for representative wavepackets using ab initio data for potentials and (transition) dipole moments. The effect of laser induced electronic transitions as well as the branching between products in the two electronic states is investigated. It is shown that by optimal choice of the laser pulse parameters the ground state process can be achieved with high efficiency (> 80%) and a vibrational state selectivity very close to 100%. For the excited state, similar results can be obtained by a two-pulse "dump-pump" strategy. The electronic branching ratio can be controlled by the frequency and the polarization of the laser pulses or the scattering energy of the collision pair.