All Figures

	Figure 1: Velocity plots of observed H2 absorption lines from the J = 0 and J = 1 rotational levels at  = 2.43127 toward Q 2343+125. Profiles of associated Si  II and Fe  II absorptions are shown in the upper panels. The best-fitting model to the system is overplotted; the location of Voigt-profile sub-components are shown as vertical dashed lines.
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In the text

	Figure 2: Absorption profiles at  = 2.4263 (taken as zero of the velocity scale) toward Q 2348-011. The positions of the seven (respectively, 13) components needed to fit the H2 (respectively, metal line) profiles are indicated by vertical dashed lines. The resulting best-fitting model to the system is overplotted.
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In the text

Figure 3: Logarithm of the molecular fraction, f = 2N(H2)/(2N(H2) + N(H  I)), versus metallicities, [X/H] = log N(X)/N(H)-log (X/H) with X either Zn, S or Si, in DLAs from the sample described in this paper ([X/H] > -1.3, see Table 1) and the sample of Ledoux et al. (2003, [X/H] < -1.3). Filled squares indicate systems in which H2 is detected. Dashed lines indicate the limits used in the text (log f = -4; [X/H] = -1.3). The dotted line shows the median of the high-metallicity sample ([X/H] = -0.7).

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In the text