  We present complete analytical and numerical results that demonstrate the
anomalous universal fluctuations of the spin-Hall conductance in chiral
materials such as graphene and topological insulators. We investigated both the
corresponding fluctuations, the Universal Fractionated and the Universal
Quantized, and also the open channels orbital number crossover between the two
regimes. In particular, we show that the Wigner-Dyson symmetries does not
properly describe such conductances and the preponderant role of the chiral
classes on the Dirac quantum dots. The results are analytical and solve
outstanding issues.
