We present new ATCA 21-cm line observations of the neutral hydrogen in the nearby radio galaxy Centaurus A. We image in detail (with a resolution down to 7 '', similar to 100 pc) the distribution of HI along the dust lane. Our data have better velocity resolution and better sensitivity than previous observations. The HI extends for a total of similar to 15 kpc. The data, combined with a titled-ring model of the disk, allow to conclude that the kinematics of the HI is that of a regularly rotating, highly warped structure down to the nuclear scale. The parameters (in particular the inclination) of our model are somewhat different from some of the previously proposed models but consistent with what was recently derived from stellar light in a central ring. The model nicely describes also the morphology of the dust lane as observed with Spitzer. There are no indications that large-scale anomalies in the kinematics exist that could be related to supplying material for the AGN. Large-scale radial motions do exist, but these are only present at larger radii (r > 6 kpc). This unsettled gas is mainly part of a tail/arm like structure. The relatively regular kinematics of the gas in this structure suggests that it is in the process of settling down into the main disk. The presence of this structure further supports the merger/interaction origin of the HI in Cen A. From the structure and kinematics we estimate a timescale of 1.6-3.2 x 10(8) yr since the merging event. No bar structure is needed to describe the kinematics of the HI. The comparison of the timescale derived from the large-scale HI structure and those of the radio structure together with the relative regularity of the HI down to the sub-kpc regions does not suggest a one-to-one correspondence between the merger and the phase of radio activity. Interestingly, the radial motions of the outer regions are such that the projected velocities are redshifted compared to the regular orbits. This means that the blueshifted absorption discovered earlier and discussed in our previous paper cannot be caused by out-moving gas at large radius projected onto the centre. Therefore, the interpretation of the blueshifted absorption, together with at least a fraction of the redshifted nuclear absorption, as evidence for a regular inner disk, still holds. Finally, we also report the discovery of two unresolved clouds detected at 5.2 and 11 kpc away (in projection) from the HI disk. They are likely an other example of a left-over of the merger that brought the HI gas.