  We wish to study the extent and subparsec scale spatial structure of
intervening quasar absorbers, mainly those involving neutral and molecular gas.
We have selected quasar absorption systems with high spectral resolution and
good S/N data, with some of their lines falling on quasar emission features. By
investigating the consistency of absorption profiles seen for lines formed
either against the quasar continuum source or on the much more extended
emission line region (ELR), we can probe the extent and structure of the
foreground absorber over the extent of the ELR (0.3-1 pc). The spatial covering
analysis provides constraints on the transverse size of the absorber and thus
is complementary to variability or photoionisation modelling studies. The
methods we used to identify spatial covering or structure effects involve line
profile fitting and curve of growth analysis.We have detected three absorbers
with unambiguous non uniformity effects in neutral gas. For one extreme case,
the FeI absorber at z_abs=0.45206 towards HE 0001-2340, we derive a coverage
factor of the ELR of at most 0.10 and possibly very close to zero; this implies
an absorber overall size no larger than 0.06 pc. For the z_abs=2.41837 CI
absorber towards QSO J1439+1117, absorption is significantly stronger towards
the ELR than towards the continuum source in several CI and CI* velocity
components pointing to factors of about two spatial variations of their column
densities and the presence of structures at the 100 au - 0.1 pc scale. The
other systems with firm or possible effects can be described in terms of
partial covering of the ELR, with coverage factors in the range 0.7 - 1. The
overall results for cold, neutral absorbers imply a transverse extent of about
five times or less the ELR size, which is consistent with other known
constraints.
