  We report on atomic gas (HI) and molecular gas (as traced by CO(2-1)) redshifted absorption features toward the nuclear regions of the closest powerful radio galaxy, Centaurus A (NGC 5128). Our HI observations using the Very Long Baseline Array allow us to discern with unprecedented sub-parsec resolution HI absorption profiles toward different positions along the 21 cm continuum jet emission in the inner 0."3 (or 5.4 pc). In addition, our CO(2-1) data obtained with the Submillimeter Array probe the bulk of the absorbing molecular gas with little contamination by emission, not possible with previous CO single-dish observations. We shed light with these data on the physical properties of the gas in the line of sight, emphasizing the still open debate about the nature of the gas that produces the broad absorption line (~55 km/s). First, the broad H I line is more prominent toward the central and brightest 21 cm continuum component than toward a region along the jet at a distance ~ 20 mas (or 0.4 pc) further from it. This suggests that the broad absorption line arises from gas located close to the nucleus, rather than from diffuse and more distant gas. Second, the different velocity components detected in the CO(2-1) absorption spectrum match well other molecular lines, such as those of HCO+(1-0), except the broad absorption line that is detected in HCO+(1-0) (and most likely related to that of the H I). Dissociation of molecular hydrogen due to the AGN seems to be efficient at distances <= 10 pc, which might contribute to the depth of the broad H I and molecular lines. 
Disentangling the circumnuclear environs of Centaurus A: II. On the   nature of the broad absorption line