  We present results from a survey of 70 radio galaxies (RGs) at redshifts
1<z<5.2 using the PACS and SPIRE on-board Herschel. Combined with existing
mid-IR photometry from Spitzer and observations obtained with LABOCA, the SEDs
of galaxies in our sample are continuously covered across 3.6-870um. The total
infrared luminosities of these RGs are such that they almost all are either
ultra-or hyper-luminous infrared galaxies. We fit the infrared SEDs with a set
of empirical templates which represent dust heated (1) by a variety of SB and
(2) by a AGN. We find that the SEDs of RGs require the dust to be heated by
both AGN and SB, but the luminosities of these two components are not strongly
correlated. Assuming empirical relations and simple physical assumptions, we
calculate the SFR, the black hole mass accretion rate (MdotBH), and the black
hole mass (MBH) for each RG. We find that the host galaxies and their BHs are
growing extremely rapidly, having SFR~100-5000 Msun/yr and MdotBH~1-100
Msun/yr. The mean sSFR of RGs at z>2.5 are higher than the sSFR of typical
star-forming galaxies over the same redshift range but are similar or perhaps
lower than the galaxy population for RGs at z<2.5. By comparing the sSFR and
the specific black hole mass accretion rate, we conclude that BHs in radio loud
AGN are already, or soon will be, overly massive compared to their host
galaxies in terms of expectations from the local MBH-MGal relation. In order to
``catch up'' with the BH, the galaxies require about an order-of magnitude more
time to grow in mass, at the observed SFRs, compared to the time the BH is
actively accreting. However, during the current cycle of activity, we argue
that this catching-up is likely to be difficult due to the short gas depletion
times. Finally, we speculate on how the host galaxies might grow sufficiently
in stellar mass to ultimately fall onto the local MBH-MGal relation.
