  We study the spin-Hall conductance fluctuations in ballistic mesoscopic
systems. We obtain universal expressions for the spin and charge current
fluctuations, cast in terms of current-current autocorrelation functions. We
show that the latter are conveniently parametrized as deformed Lorentzian shape
lines, functions of an external applied magnetic field and the Fermi energy. We
find that the charge current fluctuations show quite unique statistical
features at the symplectic-unitary crossover regime. Our findings are based on
an evaluation of the generalized transmission coefficients correlation
functions within the stub model and are amenable to experimental test.
