  With the aid of the quasiclassical Eilenberger formalism we develop a theory
of non-local electron transport across three-terminal ballistic
normal-superconducting-normal (NSN) devices with spin-active NS interfaces. The
phenomenon of crossed Andreev reflection (CAR) is known to play the key role in
such transport. We demonstrate that CAR is highly sensitive to electron spins
and yields a rich variety of properties of non-local conductance which we
describe non-perturbatively at arbitrary voltages, temperature, spin-dependent
interface transmissions and their polarizations. Our results can be applied to
multi-terminal hybrid structures with normal, ferromagnetic and half-metallic
electrodes and can be directly tested in future experiments.
