  We study the growth and saturation of the superradiant instability of a
complex, massive vector (Proca) field as it extracts energy and angular
momentum from a spinning black hole, using numerical solutions of the full
Einstein-Proca equations. We concentrate on a rapidly spinning black hole
($a=0.99$) and the dominant $m=1$ azimuthal mode of the Proca field, with real
and imaginary components of the field chosen to yield an axisymmetric
stress-energy tensor and, hence, spacetime. We find that in excess of $9\%$ of
the black hole's mass can be transferred into the field. In all cases studied,
the superradiant instability smoothly saturates when the black hole's horizon
frequency decreases to match the frequency of the Proca cloud that
spontaneously forms around the black hole.
