Using IRAM PdBI we report the detection of H2O in six new lensed ultra-luminous starburst galaxies at high redshift, discovered in the Herschel H-ATLAS survey. The sources are detected either in the 2_{02}-1_{11} or 2_{11}-2_{02} H_2O emission lines with integrated line fluxes ranging from 1.8 to 14 Jy.km/s. The corresponding apparent luminosities are mu x L_H2O ~ 3-12 x 10^8 Lo, where mu is the lensing magnification factor (3 < mu < 12). These results confirm that H2O lines are among the strongest molecular lines in such galaxies, with intensities almost comparable to those of the high-J CO lines, and same profiles and line widths (200-900 km/s) as the latter. With the current sensitivity of PdBI, H2O can therefore easily be detected in high-z lensed galaxies (with F(500um) > 100 mJy) discovered in the Herschel surveys. Correcting the luminosities for lensing amplification, L_H2O is found to have a strong dependence on the IR luminosity, varying as ~L_IR^{1.2}. This relation which needs to be confirmed with better statistics, may indicate a role of radiative (IR) excitation of the H2O lines, and implies that high-z galaxies with L_IR >~ 10^13 Lo tend to be very strong emitters in H2O, that have no equivalent in the local universe.
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