We build a sample of O vi absorption sytems in the redshift range 2.0 \lesssim z \lesssim 2.6 using high spectral resolution data of ten quasars from the VLT-UVES Large Programme . We investigate the existence of a metal-rich O vi population and define observational criteria for this class of aborbers under the assumption of photoionization . The low temperatures of nearly half of all O vi aborbers , implied by their line widths , are too low for collisional ionization to be a dominant process . We estimate the oxygen abundance under the assumption of photoionization ; a striking result is the bimodal distribution of [ O/H ] with median values close to 0.01 and 0.5 solar for the metal-poor and metal-rich populations , respectively . Using the line widths to fix the temperature or assuming a constant , low gas density does not drastically change the metallicities of the metal-rich population . We present the first estimate of the O vi column density distribution . Assuming a single power-law distribution , f ( N ) \propto N ^ { - \alpha } , yields \alpha \sim 1.7 and a normalization of f ( N ) = 2.3 \times 10 ^ { -13 } at log N ( O vi ) \sim 13.5 , both with a \sim 30 % uncertainty . The value of \alpha is similar to that found for C iv surveys , whereas the normalization factor is about ten times higher . We use f ( N ) to derive the number density per unit z and cosmic density , \Omega _ { b } ( O vi ) , selecting a limited column density range not strongly affected by incompleteness or sample variance . Comparing our results with those obtained at z \sim 0.1 for a similar range of column densities implies some decline of dn / dz with z . The cosmic O vi density derived from f ( N ) , \Omega _ { b } ( O vi ) \approx ( 3.5 \pm ^ { 3.2 } _ { 0.9 } ) \times 10 ^ { -7 } , is 2.3 times higher than the value estimated using the observed O vi sample ( of which the metal-rich population contributes \sim 35 % ) , easing the problem of missing metals at high z ( \sim 1/4 of the produced metals ) but not solving it . We find that the majority of the metal-rich absorbers are located within \sim 450 km s ^ { -1 } of strong Ly- \alpha lines and show that , contrary to the metal-poor absorbers , this population can not be in hydrostatic equilibrium . All of the O vi absorber properties imply that there are two distinct populations : metal-poor absorbers tracing the intergalactic medium and metal-rich absorbers associated with active sites of star formation and most probably linked to galactic winds .