Physical Conditions in the Broad Line Region of $z\sim3$ Quasars: A
  Photoionization Method to Derive $r_{BLR}$
  We present high S/N UV spectra for eight quasars at $z\sim3$\ obtained with
VLT/FORS. The spectra enable us to analyze in detail the strongest emission
features in the rest-frame range 1400-2000 \AA\ of each source (\ciii, \siiii,
\aliii, \siii, \civ\ and \siiv). Previous work indicates that a component of
these lines is emitted in a region with well-defined properties i.e., a high
density and low ionization emitting region). Flux ratios \aliii/\siiii,
\civ/\aliii, \siiv/\siiii, \civ/\siiv\ and \siii/\siiii\ for this region permit
us to strongly constrain electron density, ionization parameter and metallicity
through the use of diagnostic maps built from {\sc CLOUDY} simulations.
Reliable estimates of the product density times ionization parameter allow us
to derive the radius of the broad line region \rb\ from the definition of the
ionization parameter. The \rb\ estimate and the assumption of virialized
motions in the line emitting gas yields an estimate for black hole mass. We
compare our results with estimates obtained from the \rb\ -- luminosity
correlation customarily employed to estimate black hole masses of high redshift
quasars.
