We consider the problem of growing the largest supermassive black holes from stellar–mass seeds at high redshift .
Rapid growth without violating the Eddington limit requires that most mass is gained while the hole has a low spin and thus a low radiative accretion efficiency .
If , as was formerly thought , the black–hole spin aligns very rapidly with the accretion flow , even a randomly–oriented sequence of accretion events would all spin up the hole and prevent rapid mass growth .
However , using a recent result that the Bardeen–Petterson effect causes counter alignment of hole and disc spins under certain conditions , we show that holes can grow rapidly in mass if they acquire most of it in a sequence of randomly oriented accretion episodes whose angular momenta J _ { d } are no larger than the hole ’ s angular momentum J _ { h } .
Ultimately the hole has total angular momentum comparable with the last accretion episode .
This points to a picture in which the accretion is chaotic on a lengthscale of order the disc size , that is \la 0.1 pc .