  Hyper-accreting discs occur in compact-object mergers and collapsars, and may
power gamma-ray bursts (GRBs). We calculate the microscopic viscosity and
resistivity of plasma in these discs, and discuss the implications for their
global structure and evolution. In the neutrino-cooled innermost regions, the
viscosity is provided mainly by mildly degenerate electrons, while the
resistivity is modified from the Spitzer value due to the effects of both
relativity and degeneracy. The plasma behaves as an almost ideal MHD fluid.
Among the non-ideal MHD effects the Hall term is relatively the most important,
while the magnetic Prandtl number, Pr (the ratio of viscosity to resistivity),
is typically larger than unity: 10 < Pr < 6000. The outer radiatively
inefficient regions also display high Pr. Numerical simulations of the
magneto-rotational instability indicate that the saturation level and angular
momentum transport efficiency may be greatly enhanced at high Pr. If this
behaviour persists in the presence of a strong Hall effect we would expect that
hyper-accreting discs should be strongly magnetised and highly variable. The
expulsion of magnetic field that cannot be dissipated at small scales may also
favour a magnetic outflow. We note the similaries between the Prandtl number in
hyper-accreting discs and X-ray binary discs, which suggests that a comparison
between late-time activity in GRBs and X-ray binary accretion states may be
fruitful. Our results imply that the behavior of high Prandtl number MHD flows
needs to be considered in studies of hyper-accreting discs.
