  We consider an s-wave superconductor (SC) which is tunnel-coupled to two
spatially separated Luttinger liquid (LL) leads. We demonstrate that such a
setup acts as an entangler, i.e. it creates spin-singlets of two electrons
which are spatially separated, thereby providing a source of electronic
Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage,
which is smaller than the energy gap in the SC, a stationary current of
spin-entangled electrons can flow from the SC to the LL leads due to Andreev
tunneling events. We discuss two competing transport channels for Cooper pairs
to tunnel from the SC into the LL leads. On the one hand, the coherent
tunneling of two electrons into the same LL lead is shown to be suppressed by
strong LL correlations compared to single-electron tunneling into a LL. On the
other hand, the tunneling of two spin-entangled electrons into different leads
is suppressed by the initial spatial separation of the two electrons coming
from the same Cooper pair. We show that the latter suppression depends
crucially on the effective dimensionality of the SC. We identify a regime of
experimental interest in which the separation of two spin-entangled electrons
is favored. We determine the decay of the singlet state of two electrons
injected into different leads caused by the LL correlations. Although the
electron is not a proper quasiparticle of the LL, the spin information can
still be transported via the spin density fluctuations produced by the injected
spin-entangled electrons.
