  We analyze microscopically a Cooper pair splitting device in which a central
superconducting lead is connected to two weakly coupled normal leads through a
carbon nanotube. We determine the splitting efficiency at resonance in terms of
geometrical and material parameters, including the effect of spin-orbit
scattering. While the efficiency in the linear regime is limited to 50% and
decay exponentially as a function of the width of the superconducting region we
show that it can rise up to $\sim 100%$ in the non-linear regime for certain
regions of the stability diagram.
