  We discuss the formation of molecular oxygen in ultracold collisions between
hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based
on hyperspherical coordinates is employed for the calculations. Elastic,
inelastic and reactive cross sections as well as the vibrational and rotational
populations of the product O2 molecules are reported. A J-shifting
approximation is used to compute the rate coefficients. At temperatures T = 10
- 100 mK for which the OH molecules have been cooled and trapped
experimentally, the elastic and reactive rate coefficients are of comparable
magnitude, while at colder temperatures, T < 1 mK, the formation of molecular
oxygen becomes the dominant pathway. The validity of a classical capture model
to describe cold collisions of OH and O is also discussed. While very good
agreement is found between classical and quantum results at T=0.3 K, at higher
temperatures, the quantum calculations predict a larger rate coefficient than
the classical model, in agreement with experimental data for the O + OH
reaction. The zero-temperature limiting value of the rate coefficient is
predicted to be about 6.10^{-12} cm^3 molecule^{-1} s^{-1}, a value comparable
to that of barrierless alkali-metal atom - dimer systems and about a factor of
five larger than that of the tunneling dominated F + H2 reaction.
