  We present near-IR photometry and spectroscopy of 30 extremely luminous radio
and mid-IR selected galaxies. With bolometric luminosities exceeding
$\sim10^{13}$ $\rm{L_{\odot}}$ and redshifts ranging from $z = 0.880-2.853$, we
use VLT instruments X-shooter and ISAAC to investigate this unique population
of galaxies. Broad multi-component emission lines are detected in 18 galaxies
and we measure the near-IR lines $\rm{H\rm{\beta}}$,
$\text{[OIII]}\rm{\lambda}\rm{\lambda}4959,5007$ and $\rm{H\rm{\alpha}}$ in
six, 15 and 13 galaxies respectively, with 10 $\rm{Ly\alpha}$ and five CIV
lines additionally detected in the UVB arm. We use the broad
$\text{[OIII]}\rm{\lambda}5007$ emission lines as a proxy for the bolometric
AGN luminosity, and derive lower limits to supermassive black hole masses of
$10^{7.9}$-$10^{9.4}$ $\text{M}_{\odot}$ with expectations of corresponding
host masses of $10^{10.4}$-$10^{12.0}$ $\text{M}_{\odot}$. We measure
$\rm{\lambda}_{Edd}$ > 1 for eight of these sources at a $2\sigma$
significance. Near-IR photometry and SED fitting are used to compare stellar
masses directly. We detect both Balmer lines in five galaxies and use these to
infer a mean visual extinction of $A_{V}$ = 2.68 mag. Due to non-detections and
uncertainties in our $\rm{H\rm{\beta}}$ emission line measurements, we simulate
a broad $\rm{H\rm{\beta}}$ line of FWHM = 1480 $\rm{kms^{-1}}$ to estimate
extinction for all sources with measured $\rm{H\rm{\alpha}}$ emission. We then
use this to infer a mean $A_{V}=3.62$ mag, demonstrating the highly-obscured
nature of these galaxies, with the consequence of increasing our estimates of
black-hole masses by an 0.5 orders of magnitude in the most extreme and
obscured cases.
