  We perform numerical simulations of black-hole binaries to study the exchange
of spin and orbital angular momentum during the last, highly nonlinear, stages
of the coalescence process. To calculate the transfer of angular momentum from
orbital to spin, we start with two quasi-circular configurations, one with
initially non-spinning black holes, the other with corotating black holes. In
both cases the binaries complete almost two orbits before merging. We find
that, during these last orbits, the specific spin (a/m) of each horizon
increases by only 0.012 for the initially non-spinning configuration, and by
only 0.006 for the initially corotating configuration. By contrast, the
corotation value for the specific spin should increase from 0.1 at the initial
proper separation of 10M to 0.33 when the proper separation is 5M. Thus the
spin-orbit coupling is far too weak to tidally lock the binary to a corotating
state during the late-inspiral phase. We also study the converse transfer from
spin into orbital motion. In this case, we start the simulations with parallel,
highly-spinning non-boosted black holes. As the collision proceeds, the system
acquires a non-head-on orbital motion, due to spin-orbit coupling, that leads
to the radiation of angular momentum. We are able to accurately measure the
energy and angular momentum losses and model their dependence on the initial
spins.
