  We present a detailed calculation of the propagation of AGN-like ionizing
radiation through the intergalactic space. We model the ionization state of
absorbing clouds, and show that the universe will be more opaque above $4\,$Ryd
than previously estimated. Singly ionized helium in \Lya forest clouds and
Lyman-limit systems is found to be very efficient in reprocessing soft X-ray,
helium-ionizing photons into ultraviolet, hydrogen-ionizing ones. We
demonstrate that a significant fraction of the absorbed primary photons
(emitted, e.g., by quasar sources) will be reradiated by the photoionized gas
through \Lya line emission, two-photon continuum, and recombination continuum
radiation. In the light of new data and recent studies, we also reassess the
contribution of the QSOs observed in optical surveys to the UV extragalactic
background, and find that the stochastic reprocessing of quasar Lyman continuum
radiation by hydrogen and helium along the line of sight will significantly
affect the amplitude, spectral shape, and fluctuations properties of the
metagalactic flux. In a scenario in which QSOs are the primary source of
ionizing photons in the universe, the integrated \HI \Lya emission at $z=0$
from photoionized \Lya clouds and Lyman-limit systems is found to be at a level
of less than 5\% of current observational limits on the far-UV extragalactic
radiation flux. We show that $J_{912}$ increases from $\approx 10^{-23}
\uvunits$ at the present epoch to $\approx 5\times 10^{-22}\uvunits$ at
$z=2.5$. The attenuated direct quasar emission plus recombination radiation
from intergalactic gas appears to provide enough hydrogen-ionizing photons to
satisfy the proximity effect at large redshift. The \HeII/\HI ratio in the
diffuse intergalactic medium and the \Lya clouds increases from $\approx25$ at
