  We present the results of high-resolution numerical simulations of gas clouds
falling onto binary supermassive black holes to form circumbinary accretion
discs, with both prograde and retrograde cloud orbits. We explore a range of
clouds masses and cooling rates. We find that for low mass discs that cool fast
enough to fragment, prograde discs are significantly shorter-lived than similar
discs orbiting retrograde with respect to the binary. For fragmenting discs of
all masses, we also find that prograde discs fragment across a narrower radial
region. If the cooling is slow enough that the disc enters a self-regulating
gravitoturbulent regime, we find that alignment between the disc and binary
planes occurs on a timescale primarily dictated by the disc thickness. We
estimate realistic cooling times for such discs, and find that in the majority
of cases we expect fragmentation to occur. The longer lifetime of low-mass
fragmenting retrograde discs allows them to drive significant binary evolution,
and may provide a mechanism for solving the 'last parsec problem'.
