High-redshift SMBHs can grow from stellar-mass seeds via chaotic
  accretion
  Extremely massive black holes, with masses $M_{\rm BH} > 10^9 M_\odot$, have
been observed at ever higher redshifts. These results create ever tighter
constraints on the formation and growth mechanisms of early black holes. Here
we show that even the most extreme black hole known, P\=oniu\=a'ena, can grow
from a $10 M_\odot$ seed black hole via Eddington-limited luminous accretion,
provided that accretion proceeds almost continuously, but is composed of a
large number of episodes with individually-uncorrelated initial directions.
This chaotic accretion scenario ensures that the growing black hole spins
slowly, with the dimensionless spin parameter $a \lesssim 0.2$, so its
radiative efficiency is also low, $\epsilon \simeq 0.06$. If accretion is even
partially aligned, with $20-40\%$ of accretion events happening in the same
direction, the black hole spin and radiative efficiency are much higher,
leading to significantly slower growth. We suggest that the chaotic accretion
scenario can be completely falsified only if a $10^9 M_\odot$ black hole is
discovered at $z \geq 9.1$, approximately $150$~Myr before P\=oniu\=a'ena. The
space density of extreme quasars suggests that only a very small fraction,
roughly one in $4 \times 10^7$, of seed black holes need to encounter
favourable growth conditions to produce the observed extreme quasars. Other
seed black holes grow much less efficiently, mainly due to lower duty cycles,
so are much more difficult to detect.
