The comoving mass density of Mg II from z ̃ 2 to 5.5

We present the results of a survey for intervening MgII absorbers in the redshift range z similar or equal to 2-6 in the foreground of four high-redshift quasar spectra, 5.79 <= z(em) <= 6.133, obtained with the European Southern Observatory Very Large Telescope X-Shooter. We visually identify 52 MgII absorption systems and perform a systematic completeness and false positive analysis. We find 24 absorbers at >= 5 sigma significance in the equivalent width range 0.117 <= W-2796 <= 3.655 angstrom with the highest redshift absorber at z = 4.89031 +/- 4x10(-5). For weak (W-2796 <= 0.3 angstrom) systems, we measure an incidence rate dN/dz = 1.35 +/- 0.58 at < z > = 2.34 and find that it almost doubles to dN/dz = 2.58 +/- 0.67 by < z > = 4.81. The number of weak absorbers exceeds the number expected from an exponential fit to stronger systems (W-2796 > 0.3 angstrom). We find that there must be significant evolution in the absorption halo properties of MgII absorbers with W-2796 > 0.1 angstrom by < z > = 4.77 and/or that they are associated with galaxies with luminosities beyond the limits of the current luminosity function at z similar to 5. We find that the incidence rate of strong MgII absorbers (W-2796 > 1.0 angstrom) can be explained if they are associated with galaxies with L >= 0.29L* and/or their covering fraction increases. If they continue to only be associated with galaxies with L >= 0.50L* then their physical cross-section (sigma(phys)) increases from 0.015 Mpc(2) at z = 2.3-0.041 Mpc(2) at < z > = 4.77. We measure Omega(Mg) (II) = 2.1(-0.6)(+6.3) x 10(-8), 1.9(-0.2)(+2.9) x 10(-8) and 3.9(-2.4)(+7.1) x 10(-7) at < z > = 2.48, 3.41 and 4.77, respectively. At < z > = 4.77, Omega(Mg) (II) exceeds the value expected from Omega(H) (I) estimated from the global metallicity of damped Ly alpha systems (DLAs) at z similar or equal to 4.85 by a factor of similar to 44 suggesting that either MgII absorbers trace both ionized and neutral gas and/or are more metal rich than the average DLA at this redshift.