The deep OB star population in Carina from the VST Photometric H$\alpha$
  Survey (VPHAS+)
  Massive OB stars are critical to the ecology of galaxies, and yet our
knowledge of OB stars in the Milky Way, fainter than $V \sim 12$, remains
patchy. Data from the VST Photometric H$\alpha$ Survey (VPHAS+) permit the
construction of the first deep catalogues of blue excess-selected OB stars,
without neglecting the stellar field. A total of 14900 candidates with 2MASS
cross-matches are blue-selected from a 42 square-degree region in the Galactic
Plane, capturing the Carina Arm over the Galactic longitude range $282^{\circ}
\lesssim \ell \lesssim 293^{\circ}$. Spectral energy distribution fitting is
performed on these candidates' combined VPHAS+ $u,g,r,i$ and 2MASS $J,H,K$
magnitudes. This delivers: effective temperature constraints, statistically
separating O from early-B stars; high-quality extinction parameters, $A_0$ and
$R_V$ (random errors typically $< 0.1$). The high-confidence O-B2 candidates
number 5915 and a further 5170 fit to later B spectral type. Spectroscopy of
276 of the former confirms 97% of them. The fraction of emission line stars
among all candidate B stars is 7--8% . Greyer ($R_V > 3.5$) extinction laws are
ubiquitous in the region, over the distance range 2.5--3 kpc to $\sim$10~kpc.
Near prominent massive clusters, $R_V$ tends to rise, with particularly large
and chaotic excursions to $R_V \sim 5$ seen in the Carina Nebula. The data
reveal a hitherto unnoticed association of 108 O-B2 stars around the O5If$+$
star LSS 2063 ($\ell = 289.77^{\circ}$, $b = -1.22^{\circ}$). Treating the OB
star scale-height as a constant within the thin disk, we find an orderly mean
relation between extinction ($A_0$) and distance in the Galactic longitude
range, $287.6^{\circ} < \ell < 293.5^{\circ}$, and infer the subtle onset of
thin-disk warping. A halo around NGC 3603, roughly a degree in diameter, of
$\sim$500 O-B2 stars with $4 < A_0 (\rm{mag}) < 7$ is noted.
