  The prediction of the spin of the black hole resulting from the merger of a
generic black-hole binary system is of great importance to study the
cosmological evolution of supermassive black holes. Several attempts have been
recently made to model the spin via simple expressions exploiting the results
of numerical-relativity simulations. Here, I first review the derivation of a
formula, proposed in Barausse & Rezzolla, Apj 704 L40, which accurately
predicts the final spin magnitude and direction when applied to binaries with
separations of hundred or thousands of gravitational radii. This makes my
formula particularly suitable for cosmological merger-trees and N-body
simulations, which provide the spins and angular momentum of the two black
holes when their separation is of thousands of gravitational radii. More
importantly, I investigate the physical reason behind the good agreement
between my formula and numerical relativity simulations, and nail it down to
the fact that my formula takes into account the post-Newtonian precession of
the spins and angular momentum in a consistent manner.
