  (abridged) We consider the effect of stellar remnants on the interstellar
medium of a massive star cluster following the initial burst of star formation.
We argue that accretion onto stellar-mass black holes (BHs) is an effective
mechanism for rapid gas depletion in clusters of all masses, as long as they
contain progenitor stars more massive than \gtrsim 50\msun. This scenario is
attractive for the progenitor systems of present-day massive globular clusters
(GCs) which likely had masses M \gtrsim 10^7\msun. In such clusters, supernovae
and stellar winds cannot provide a plausible explanation for the sudden removal
of the primordial gas reservoir that is required to explain their complex
chemical enrichment history.
  In order to consider different regimes in the gas accretion rate onto
stellar-mass BHs, we consider both the Bondi-Hoyle and Eddington
approximations. For either model, our results show that the gas can be
significantly depleted within only a few tens of Myrs. This process will affect
the distribution of BH masses, and may accelerate the dynamical decoupling of
the BH population and, ultimately, their dynamical ejection. Moreover, the
timescales for gas depletion are sufficiently short that the accreting BHs
could significantly affect the chemistry of subsequent star formation episodes.
  The gas depletion times and final mass in BHs are sensitive to the assumed
model for the accretion rate, and to the initial mass of the most massive BH
which, in turn, is determined by the upper mass cut-off of the stellar IMF. Our
results imply that the remnant accretion history can have an important bearing
on the observed present-day cluster mass-to-light ratio. In particular, we show
that an increase of the upper mass cut-off with decreasing metallicity could
contribute to the observed anti-correlation between the mass-to-light ratio and
the metallicity of GCs.
