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Retrograde accretion is that of an accretion disk rotating in the opposite direction from the accreting body's rotation. Whether retrograde or not, the rotation axes of the accreting body and the accretion disk can also be other than parallel. The typical direction of a body's accretion is prograde, the body and its accreting material both resulting from a single cloud, retaining the cloud's rotation.
A theory is that some central galaxy SMBH's undergo retrograde accretion (retrograde accreting black holes, i.e., with retrograde accretion disks), due to the black hole rotating in the opposite direction than the galaxy. The theory further hypothesizes such accretion can be a factor in generating extreme emission from some galaxies, a reason why active galactic nuclei (AGNs) appear to fall into two classes: typical versus very bright. Such a situation is presumed to come about from galaxy mergers placing a SMBH in a galaxy rotating in the opposite direction.
Such accretion slows the SMBH's rotation, and sufficient such accretion reverses it. If the SMBH has doubled in mass over its lifetime, a past such reversal is a definite possibility: if the accretion adding this mass was initially retrograde, the disk could have had the angular momentum to reverse the black hole's rotation. This is one possible mechanism for an observed reduction in the number of quasars over time (c.f., the Meier paradox): that mergers were common once, and sufficient time has passed to reverse the rotation of many of the SMBH's.