  We study the properties of the "spin quantum Hall fluid" - a novel spin phase
with quantized spin Hall conductance that is potentially realizable in
superconducting systems with unconventional pairing symmetry. A simple
realization is provided by a $d_{x^2-y^2} + id_{xy}$ superconductor which we
argue has a dimensionless spin Hall conductance equal to two. A theory of the
edge states of the $d_{x^2-y^2}+id_{xy}$ superconductor is developed. The
properties of the transition to a phase with vanishing spin Hall conductance
induced by disorder are considered. We construct a description of this
transition in terms of a supersymmetric spin chain, and use it to numerically
determine universal properties of the transition. We discuss various possible
experimental probes of this quantum Hall physics.
