  Rapid inflows associated with early galaxy formation lead to the accumulation
of self-gravitating gas in the centers of proto-galaxies. Such gas
accumulations are prone to non-axisymmetric instabilities, as in the well-known
Maclaurin sequence of rotating ellipsoids, which are accompanied by a
catastrophic loss of angular momentum (J). Self-gravitating gas is also
intuitively associated with star formation. However, recent simulations of the
infall process display highly turbulent continuous flows. We propose that
J-transfer, which enables the inflow, also suppresses fragmentation.
Inefficient J loss by the gas leads to decay of turbulence, triggering global
instabilities and renewed turbulence driving. Flow regulated in this way is
stable against fragmentation, whilst staying close to the instability threshold
for bar formation -- thick self-gravitating disks are prone to global
instabilities before they become unstable locally. On smaller scales, the
fraction of gravitationally unstable matter swept up by shocks in such a flow
is a small and decreasing function of the Mach number. We conclude
counterintuitively that gas able to cool down to a small fraction of its virial
temperature will not fragment as it collapses. This provides a venue for
supermassive black holes to form via direct infall, without the intermediary
stage of forming a star cluster. Some black holes could have formed or grown in
massive halos at low redshifts. Thus the fragmentation is intimately related to
J redistribution within the system: it is less dependent on the molecular and
metal cooling but is conditioned by the ability of the flow to develop virial,
supersonic turbulence.
