  [Abridged] We present new VLT ISAAC spectra for 30 quasars, which we combine
with previous data to yield a sample of 53 intermediate redshift (z ~ 0.9 -
3.0) sources. The sample is used to explore properties of prominent lines in
the Hbeta spectral region of these very luminous quasars. We find two major
trends: (1) a systematic increase of minimum FWHM Hbeta with luminosity
(discussed in a previous paper). This lower FWHM envelope is best fit assuming
that the narrowest sources radiate near the Eddington limit, show line emission
from a virialized cloud distribution, and obey a well defined broad line region
size vs. luminosity relation. (2) A systematic decrease of equivalent width of
[OIII] (from W ~ 15 to ~ 1 A) with increasing source bolometric luminosity
(from log L ~ 43 to log L ~ 49). Further identified trends required
discrimination between so-called Population A and B sources. We generate median
composite spectra in six luminosity bins Pop. A sources show reasonably
symmetric Lorentzian Hbeta profiles at all luminosities while Pop. B sources
require two component fits involving an unshifted broad and a redshifted very
broad component. Very broad Hbeta increases in strength with increasing L while
the broad component remains constant resulting in an apparent "Baldwin effect"
with equivalent width decreasing from W ~ 80 to ~ 20 A over our sample
luminosity range. The roughly constant equivalent width shown by the Hbeta very
broad component implies production in optically-thick, photoionized gas. The
onset of the redshifted very broad component appears to be a critical change
that occurs near the Pop. A-B boundary at FWHM Hbeta ~ 4000 km/s which we
relate to a critical Eddington ratio (~ 0.2 +/- 0.1).
