We use the spectra of 73 quasars (1.5=<z=<5) from the VLT UVES archive to catalogue and study narrow absorption lines (NALs) that are physically associated with (intrinsic to) the quasars. We identify 410 NAL systems containing CIV, NV, and/or SiIV doublets. Based on the assumption that only systems intrinsic to the quasar can exhibit partial coverage of the background source(s), we identify 34 reliably intrinsic NAL systems and 11 systems that are potentially intrinsic, as well as 4 mini-broad absorption lines (BALs) and 1 BAL. The minimum fraction of quasars with at least one intrinsic system is shown to be 38 per cent. We identify intrinsic NALs with a wide range of properties, including apparent ejection velocity, coverage fraction, and ionization level. There is a continuous distribution of properties, rather than discrete families, ranging from partially covered CIV systems with black Ly{alpha} and with a separate low-ionization gas phase to partially covered NV systems with partially covered Ly{alpha} and without detected low-ionization gas. Even more highly ionized associated and intrinsic absorption systems (OVI, NeVIII, and MgX doublets) have been presented in separate studies; these may represent an extension of the above sequence. We also use the properties of the NALs in conjunction with recent models of accretion disc winds that predict the origins of the absorbing gas in order to determine the model that best characterizes our sample. Additionally, we construct a model describing the spatial distributions, geometries, and varied ionization structures of intrinsic NALs.