  We study the properties of HI gas in the outer regions (~2r_25) of a spiral
galaxy, UGC 00439 (z = 0.01769), using HI 21-cm absorption towards different
components of an extended background radio source, J0041$-$0043 (z = 1.679).
The radio source exhibits a compact core coincident with the optical quasar and
two lobes separated by ~7 kpc, all at an impact parameter ~25 kpc. The HI 21-cm
absorption detected towards the southern lobe is found to extend over ~2 kpc^2.
The absorbing gas shows sub-kpc-scale structures with the line-of-sight
velocities dominated by turbulent motions. Much larger optical depth variations
over 4-7 kpc-scale are revealed by the non-detection of HI 21-cm absorption
towards the radio core and the northern lobe, and the detection of NaI and CaII
absorption towards the quasar. This could reflect a patchy distribution of cold
gas in the extended HI disc. We also detect HI 21-cm emission from UGC 00439
and two other galaxies within ~150 kpc to it, that probably form an interacting
group. However, no HI 21-cm emission from the absorbing gas is detected.
Assuming a linear extent of ~4 kpc, as required to cover both the core and the
southern lobe, we constrain the spin temperature <~300 K for the absorbing gas.
The kinematics of the gas and the lack of signatures of any ongoing in situ
star formation are consistent with the absorbing gas being at the kinematical
minor axis and corotating with the galaxy. Deeper HI 21-cm observations would
help to map in greater detail both the large- and small-scale structures in the
HI gas associated with UGC 00439.
