  A superconductor connected to normal leads allows to generate
Einstein-Podolsky-Rosen pairs by Cooper pair splitting. It has been realized
with quantum dots either defined in carbon nanotubes or InAs nanowires. After
establishing the presence of Cooper pair splitting in such devices new works
have invesigated the effects of a finite potential difference between the
quantum dots to improve and characterize the efficiency of Cooper pair
splitting. In this paper we present a generic model for Cooper pair splitting
and develop two minimal models specifically for the two experimental
realisations and compare them to experimental data. In addition we also explore
the relation of nonlocal charge transfer to positive current cross correlation
of currents and discuss the temperature dependence of Cooper pair splitting.
