We present a detailed analysis of three extremely strong intervening damped Lyman- \alpha systems ( ESDLAs , with \log N ( { H \textsc { i } } ) \geq 21.7 ) observed towards quasars with the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope .
We measure overall metallicities of [ Zn/H ] \sim -1.2 , -1.3 and -0.7 at respectively z _ { abs } =2.34 towards SDSS J214043.02 - 032139.2 ( \log N ( { H \textsc { i } } ) = 22.4 \pm 0.1 ) , z _ { abs } =3.35 towards SDSS J145646.48 + 160939.3 ( \log N ( { H \textsc { i } } ) = 21.7 \pm 0.1 ) and z _ { abs } =2.25 towards SDSS J015445.22 + 193515.8 ( \log N ( { H \textsc { i } } ) = 21.75 \pm 0.15 ) .
Iron depletion of about a factor 15 compared to volatile elements is seen in the DLA towards J2140 - 0321 , while the other two show deletion typical of known DLAs .
We detect H _ { 2 } towards J2140 - 0321 ( \log N ( H _ { 2 } ) = 20.13 \pm 0.07 ) and J1456 + 1609 ( \log N ( H _ { 2 } ) = 17.10 \pm 0.09 ) and argue for a tentative detection towards J0154 + 1935 .

Absorption from the excited fine-structure levels of O i , C i and Si ii are detected in the system towards J2140 - 0321 , that has the largest H i column density detected so far in an intervening DLA .
This is the first detection of O i fine-structure lines in a QSO-DLA , that also provides us a rare possibility to study the chemical abundances of less abundant atoms like Co and Ge .
Simple single phase photo-ionisation models fail to reproduce all the observed quantities .
Instead , we suggest that the cloud has a stratified structure : H _ { 2 } and C i likely originate from both a dense ( \log n _ { H } \sim 2.5 - 3 ) cold ( 80 K ) and warm ( 250 K ) phase containing a fraction of the total H i while a warmer ( T > 1000 K ) phase probably contributes significantly to the high excitation of O i fine-structure levels .
The observed C i /H _ { 2 } column density ratio is surprisingly low compared to model predictions and we do not detect CO molecules : this suggests a possible underabundance of C by 0.7 dex compared to other alpha elements .
The absorber could be a photo-dissociation region close to a bright star ( or a star cluster ) where higher temperature occurs in the illuminated region .
Direct detection of on-going star formation through e.g .
NIR emission lines in the surrounding of the gas would enable a detailed physical modelling of the system .