We are engaged in a programme of imaging with the STIS and NICMOS (NIC2) instruments aboard the Hubble Space Telescope (HST), to search for the galaxy counterparts of 18 high-redshift z>1.75 damped Lya absorption lines and 5 Lyman-limit systems seen in the spectra of 16 target quasars. This paper presents the results of the imaging campaign with the NIC2 camera. We describe the steps followed in reducing the data and combining in mosaics, and the methods used for subtracting the image of the quasar in each field, and for constructing error frames that include the systematic errors associated with the psf subtraction. To identify candidate counterparts, that are either compact or diffuse, we convolved the image and variance frames with circular top-hat filters of diameter 0.45 and 0.90 arcsec respectively, to create frames of summed S/N within the aperture. For each target quasar we provide catalogues listing positions and aperture magnitudes of all sources within a square of side 7.5 arcsec centred on the quasar, detected at S/N>6. We find a total of 41 candidates of which three have already been confirmed spectroscopically as the counterparts. We provide the aperture magnitude detection limits as a function of impact parameter, for both detection filters, for each field. The average detection limit for compact (diffuse) sources is H(AB)=25.0 (24.4) at an angular separation of 0.56 arcsec (0.79 arcsec) from the quasar, improving to H(AB)=25.5 (24.8) at large angular separations. For the brighter sources we have measured the half-light radius and the n parameter of the best-fit deconvolved Sersic-law surface-brightness profile, and the ellipticity and orientation.
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