  We investigate spin-dependent transport in three--terminal mesoscopic
cavities with spin--orbit coupling. Focusing on the inverse spin Hall effect,
we show how injecting a pure spin current or a polarized current from one
terminal generates additional charge current and/or voltage across the two
output terminals. This allows to extract the spin conductance of the cavity
from two purely electrical measurements on the output. We use random matrix
theory to show that the spin conductance of chaotic ballistic cavities
fluctuates universally about zero mesoscopic average and describe experimental
implementations of mesoscopic spin to charge current converters.
