  We present results of a blind survey of Lyman limit systems (LLSs) detected
in absorption against 105 quasars at z~3 using the blue sensitive MagE
spectrograph at the Magellan Clay telescope. By searching for Lyman limit
absorption in the wavelength range ~3000-4000A, we measure the number of LLSs
per unit redshift l(z)=1.21+/-0.28 at z~2.8. Using a stacking analysis, we
further estimate the mean free path of ionizing photons in the z~3 Universe
lambda^912 = 100+/-29 Mpc/h_70.4. Combined with our LLS survey, we conclude
that systems with log N_HI >= 17.5 cm^-2 contribute only ~40% to the observed
mean free path at these redshifts. Further, with the aid of photo-ionization
modeling, we infer that a population of ionized and metal poor systems is
likely required to reproduce the metal line strengths observed in a composite
spectrum of 20 LLSs with N_HI = 17.5-19 cm^-2 at z~2.6-3.0. Finally, with a
simple toy model, we deduce that gas in the halos of galaxies can alone account
for the totality of LLSs at z<~3, but a progressively higher contribution from
the intergalactic medium is required beyond z~3.5. We also show how the weakly
evolving number of LLSs per unit redshift at z<~3 can be modeled either by
requiring that the spatial extent of the circumgalactic medium is redshift
invariant in the last ~10 Gyr of cosmic evolution or by postulating that LLSs
arise in halos that are rare fluctuations in the density field at each
redshift.
