We have identified 469 MgII doublet systems having W_r >= 0.02 {AA} in 252 Keck/HIRES and UVES/VLT quasar spectra over the redshift range 0.1 < z < 2.6. Using the largest sample yet of 188 weak MgII systems (0.02 {AA} <= W_r < 0.3 {AA}), we calculate their absorber redshift path density, dN/dz. We find clear evidence of evolution, with dN/dz peaking at z ~ 1.2, and that the product of the absorber number density and cross section decreases linearly with increasing redshift; weak MgII absorbers seem to vanish above z ~ 2.7. If the absorbers are ionized by the UV background, we estimate number densities of 10^6 - 10^9 per Mpc^3 for spherical geometries and 10^2 - 10^5 per Mpc^3 for more sheetlike geometries. We also find that dN/dz toward intrinsically faint versus bright quasars differs significantly for weak and strong (W_r >= 1.0 {AA}) absorbers. For weak absorption, dN/dz toward bright quasars is ~ 25% higher than toward faint quasars (10 sigma at low redshift, 0.4 <= z <= 1.4, and 4 sigma at high redshift, 1.4 < z <= 2.34). For strong absorption the trend reverses, with dN/dz toward faint quasars being ~ 20% higher than toward bright quasars (also 10 sigma at low redshift and 4 sigma at high redshift). We explore scenarios in which beam size is proportional to quasar luminosity and varies with absorber and quasar redshifts. These do not explain dN/dzs dependence on quasar luminosity.
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