  We study the conductance of normal-superconducting quantum dots with strong
spin-orbit scattering, coupled to a source reservoir using a single-mode
spin-filtering quantum point contact. The choice of the system is guided by the
aim to study triplet Andreev reflection without relying on half metallic
materials with specific interface properties. Focusing on the zero temperature,
zero-bias regime, we show how dephasing due to the presence of a voltage probe
enables the conductance, which vanishes in the quantum limit, to take nonzero
values. Concentrating on chaotic quantum dots, we obtain the full distribution
of the conductance as a function of the dephasing rate. As dephasing gradually
lifts the conductance from zero, the dependence of the conductance fluctuations
on the dephasing rate is nonmonotonic. This is in contrast to chaotic quantum
dots in usual transport situations, where dephasing monotonically suppresses
the conductance fluctuations.
