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 nonaxisymmetric 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, while 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/metal cooling but is conditioned by the ability of the flow to develop virial, supersonic turbulence.