We present new HST/STIS observations of Centaurus A. [SIII] 9533A was used to study the kinematics in the nuclear region with a 0.1 spatial resolution. The STIS data and the VLT/ISAAC spectra by Marconi et al. (2001) provide independent and consistent measures of the BH mass, which are in agreement with our previous estimate based on the ISAAC data alone: MBH=(1.1+/-0.1) 10^8 Msun for a disk inclination of i=25deg or or MBH=(6.5+/-0.7) 10^7 Msun for i=35deg, the largest i value allowed by the data. We find that the choice of the intrinsic surface brightness distribution, a crucial element in the modeling, has no effects on MBH but has a large impact on the gas velocity dispersion. A mismatch between the observed and model velocity dispersion is not necessarily an indication of non-circular motions or kinematically hot gas, but is as easily due to an inaccurate computation arising from too course a model grid, or the adoption of an intrinsic brightness distribution which is too smooth. The observed velocity dispersion, line profiles and the higher order moments in the Hermite expansion, h_3 and h_4, are consistent with emission from a rotating disk. Results from gas kinematical estimate are in good agreement with a recent stellar dynamical estimate of MBH. The BH mass in Centaurus A agrees with the correlation with infrared luminosity and mass of the host spheroid but is not in disagreement with the stellar velocity dispersion if one takes into account the intrinsic scatter of the MBH-sigma correlation. Finally, using HST data we can constrain the size of any cluster of dark objects alternative to a BH to r<0.035 (~0.6pc). Thus Centaurus A ranks among the best cases for supermassive Black Holes in galactic nuclei. (ABRIDGED)
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