  We present an analysis of the AGN broad-line regions of 6 powerful radio
galaxies at z>~2 (HzRGs) with rest-frame optical imaging spectroscopy obtained
at the VLT. All galaxies have luminous (L(H-alpha)=few x 10^44 erg s^-1),
spatially unresolved H-alpha line emission with FWHM>= 10,000 km s^-1 at the
position of the nucleus, suggesting their AGN are powered by supermassive black
holes with masses of few x 10^9 M_sun and accretion luminosities of a few
percent of the Eddington luminosity. In two galaxies we also detect the BLRs in
H-beta, suggesting relatively low extinction of A_V~1 mag, which agrees with
constraints from X-ray observations. By relating black hole and bulge mass, we
find a possible offset towards higher black-hole masses of at most ~0.6 dex
relative to nearby galaxies at a given host mass, although each individual
galaxy is within the scatter of the local relationship. If not entirely from
systematic effects, this would then suggest that the masses of the host
galaxies have increased by at most a factor ~4 since z~2 relative to the
black-hole masses, perhaps through accretion of satellite galaxies or because
of a time lag between star formation in the host galaxy and AGN fueling. We
also compare the radiative and mechanical energy output (from jets) of our
targets with predictions of recent models of "synthesis" or "grand unified" AGN
feedback, which postulate that AGN with similar radiative and mechanical energy
output rates to those found in our HzRGs may be nearing the end of their period
of active growth. We discuss evidence that they may reach this stage at the
same time as their host galaxies.
