Using data from the Sloan Digital Sky Survey data release 3 (SDSS DR3) we investigate how narrow (<700km/s) CIV and MgII quasar absorption line systems are distributed around quasars. The CIV absorbers lie in the redshift range 1.6 < z < 4 and the MgII absorbers in the range 0.4<z<2.2. By correlating absorbers with quasars on different but neighbouring lines-of-sight, we measure the clustering of absorbers around quasars on comoving scales between 4 and 30Mpc. The observed comoving correlation lengths are r_o~5h^-1Mpc, similar to those observed for bright galaxies at these redshifts. Comparing with correlations between absorbers and the quasars in whose spectra they are identified then implies: (i) that quasars destroy absorbers to comoving distances of ~300kpc (CIV) and ~800kpc (MgII) along their lines-of-sight; (ii) that >40% of CIV absorbers within 3,000km/s of the QSO are not a result of large-scale clustering but rather are directly associated with the quasar itself; (iii) that this intrinsic absorber population extends to outflow velocities of order 12,000km/s; (iv) that this outflow component is present in both radio-loud and radio-quiet quasars; and (v) that a small high-velocity outflow component is observed in the MgII population, but any further intrinsic absorber component is undetectable in our clustering analysis. We also find an indication that absorption systems within 3,000km/s are more abundant for radio-loud than for radio-quiet quasars. This suggests either that radio-loud objects live in more massive halos, or that their radio activity generates an additional low-velocity outflow, or both.