Can binary mergers produce maximally spinning black holes?

Gravitational waves carry away both energy and angular momentum as binary black holes inspiral and merge. The relative efficiency with which they are radiated determines whether the final black hole of mass M_f and spin S_f saturates the Kerr limit (χ_f≡S_f/M_f²≤1). Extrapolating from the test-particle limit, we propose expressions for S_f and M_f for mergers with initial spins aligned or anti-aligned with the orbital angular momentum. We predict the the final spin at plunge for equal-mass nonspinning binaries to better than 1%, and that equal-mass maximally spinning aligned mergers lead to nearly maximally spinning final black holes (χ_f≃0.9988). We also find black holes can always be spun up by aligned mergers provided the mass ratio is small enough.