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 Ly \alpha 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″ 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 { \mathrm { H } _ { AB } } = 25.0 ( 24.4 ) at an angular separation of 0.56 \arcsec ( 0.79 \arcsec ) from the quasar , improving to { \mathrm { 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 .