  We consider transport in a three terminal device attached to one
superconducting and two normal metal terminals, using the circuit theory of
mesoscopic superconductivity. We compute the nonlocal conductance of the
current out of the first normal metal terminal in response to a bias voltage
between the second normal metal terminal and the superconducting terminal. The
nonlocal conductance is given by competing contributions from crossed Andreev
reflection and electron cotunneling, and we determine the contribution from
each process. The nonlocal conductance vanishes when there is no resistance
between the superconducting terminal and the device, in agreement with previous
theoretical work. Electron cotunneling dominates when there is a finite
resistance between the device and the superconducting reservoir. Decoherence is
taken into account, and the characteristic timescale is the particle dwell
time. This gives rise to an effective Thouless energy. Both the conductance due
to crossed Andreev reflection and electron cotunneling depend strongly on the
Thouless energy. We suggest to experimentally determine independently the
conductance due to crossed Andreev reflection and electron cotunneling in
measurement of both energy and charge flow into one normal metal terminal in
response to a bias voltage between the other normal metal terminal and the
superconductor.
