  Accretion discs around super-massive black holes (SMBH) not only power active
galactic nuclei (AGNs), but also host single and binary embedded stellar-mass
black holes (EBHs) that grow rapidly from gas accretion. The merger of these
EBHs provides a promising mechanism for the excitation of some gravitational
wave events observed by LIGO-Virgo, especially those with source masses
considerably larger than isolated stellar-mass black hole binaries. In addition
to their mass and mass-ratio distribution, their hitherto enigmatic small
spin-parameters chi_effective carry important clues and stringent constraints
on their formation channels and evolutionary pathways. Here we show that,
between each coalescence, the typical rapid spin of the merged EBHs is
suppressed by their subsequent accretion of gas from a turbulent environment,
due to its ability to randomize the flow's spin orientation with respect to
that of the EBHs on an eddy-turnover timescale. This theory provides supporting
evidence for the prolificacy of EBH mergers and suggests that their mass growth
may be dominated by gas accretion rather than their coalescence in AGN discs.
