We present results from a survey of weak MgII absorbers in the VLT/UVES spectra of 81 QSOs obtained from the ESO archive. In this survey, we identified 112 weak MgII systems within the redshift interval 0.4 < z < 2.4 with 86% completeness down to a rest-frame equivalent width of W_r(2796) = 0.02A, covering a cumulative redshift path length of deltaZ=77.3. From this sample, we estimate that the number of weak absorbers per unit redshift dN/dz increases from 1.06 +/- 0.04 at <z>=1.9 to 1.76 +/- 0.08 at <z>=1.2 and thereafter decreases to 1.51 +/- 0.09 at <z>=0.9 and 1.06 +/- 0.10 at <z>=0.6. Thus we find evidence for an evolution in the population of weak MgII absorbers, with their number density peaking at z=1.2. We also determine the equivalent width distribution of weak systems at <z>=0.9 and <z>=1.9. At 0.4 < z < 1.4, there is evidence for a turnover from a powerlaw of the form n(W_r) propto W_r^{-1.04} at W_r(2796) < 0.1A. This turnover is more extreme at 1.4 < z < 2.4, where the equivalent width distribution is close to an extrapolation of the exponential distribution function found for strong MgII absorbers. Based on these results, we discuss the possibility that some fraction of weak MgII absorbers, particularly single cloud systems, are related to satellite clouds surrounding strong MgII systems. These structures could also be analogs to Milky Way high velocity clouds. In this context, the paucity of high redshift weak MgII absorbers is caused by a lack of isolated accreting clouds on to galaxies during that epoch.
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