We study the dust depletion pattern in eight well separated components of the z _ { abs } = 1.973 , log N ( H i ) = 20.83 , damped Lyman- \alpha system toward Q 0013 - 004 , four of which have detectable H _ { 2 } absorption .
The apparent correlation between the abundance ratios [ Fe/S ] and [ Si/S ] in the components indicates that the abundance pattern is indeed due to dust-depletion .
In particular , we find evidence for depletion similar to what is observed in cold gas of the Galactic disk ( [ Fe/Zn ] = - 1.59 , [ Fe/S ] = - 1.74 , [ Zn/S ] = - 0.15 , [ Si/S ] = - 0.85 ) in one of the weakest components in which molecular hydrogen is detected with log N ( H _ { 2 } ) \sim 16.5 .
This is the first time such a large depletion is seen in a DLA system .
Extinction due to this component is negligible owing to small total H i column density , log N ( H i ) \leq 19.4 .
This observation supports the possibility that current samples of DLA systems might be biased against the presence of cold and dusty gas along the line of sight .

The overall metallicities of this peculiar DLA system in which O i and C ii are spread over \sim 1050 km s ^ { -1 } are [ P/H ] = - 0.64 , [ Zn/H ] = - 0.74 and [ S/H ] = - 0.82 relative to solar .
The sub-DLA system at z _ { abs } = 1.96753 has [ P/H ] > 0.06 , [ Zn/H ] > - 0.02 and [ S/H ] > - 0.18 .
The overall molecular fraction is in the range - 2.7 < log f < - 0.6 , which is the highest value found for DLA systems .
H _ { 2 } is detected in four components at - 615 , - 480 , 0 and 85 km s ^ { -1 } relative to the strongest component at z _ { abs } = 1.97296 .
CO is not detected ( log N ( CO ) / N ( H i ) < - 8 ) and HD could be present at z _ { abs } = 1.97380 .

We show that the presence of H _ { 2 } is closely related to the physical conditions of the gas : high particle density together with low temperature .
The observed excitation of high J H _ { 2 } levels and the molecular fraction show large variations from one component to the other suggesting that the UV radiation field is highly inhomogeneous throughout the system .
Gas pressure , estimated from C i absorptions , is larger than what is observed in the ISM of our Galaxy .
This , together with the complex kinematics , suggests that part of the gas is subject to high compression due to either collapse , merging and/or supernovae explosions .
This is probably a consequence of intense star-formation activity in the vicinity of the absorbing gas .