The sustainable growth of the first black holes
  Super-Eddington accretion has been suggested as a possible formation pathway
of $10^9 \, M_\odot$ supermassive black holes (SMBHs) 800 Myr after the Big
Bang. However, stellar feedback from BH seed progenitors and winds from BH
accretion disks may decrease BH accretion rates. In this work, we study the
impact of these physical processes on the formation of $z \sim 6$ quasar,
including new physical prescriptions in the cosmological, data-constrained
semi-analytic model GAMETE/QSOdust. We find that the feedback produced by the
first stellar progenitors on the surrounding does not play a relevant role in
preventing SMBHs formation. In order to grow the $z \gtrsim 6$ SMBHs, the
accreted gas must efficiently lose angular momentum. Moreover disk winds,
easily originated in super-Eddington accretion regime, can strongly reduce duty
cycles. This produces a decrease in the active fraction among the progenitors
of $z\sim6$ bright quasars, reducing the probability to observe them.
