  East and Pretorius (arXiv:1704.04791) have successfully evolved, using fully
non-linear numerical simulations, the superradiant instability of the Kerr
black hole (BH) triggered by a massive, complex vector field. Evolutions
terminate in stationary states of a vector field condensate synchronised with a
rotating BH horizon. We show these end points are fundamental states of Kerr
BHs with synchronised Proca hair. Motivated by the "experimental data" from
these simulations we suggest a universal (i.e. field-spin independent),
analytic model for the subset of BHs with sychronised hair that possess a
quasi-Kerr horizon, applicable in the weak hair regime. Comparing this model
with fully non-linear numerical solutions of BHs with synchronised scalar or
Proca hair, we show the model is accurate for hairy BHs that may emerge
dynamically from superradiance, whose domain we identify.
