Aim: To extend the investigations of ultra-compact dwarf galaxies (UCDs) beyond the well studied Fornax and Virgo clusters. Methods: We measured spectroscopic redshifts of about 400 compact object candidates with 19.2 < V < 22.4 mag in the central region of the Centaurus galaxy cluster (d=43Mpc), using VIMOS@VLT. The luminosity range of the candidates covers that of bright globular clusters (GCs) and of UCDs in Fornax and Virgo. Results: We confirm the cluster membership of 27 compact objects, covering an absolute magnitude range -12.2 < M_V < -10.9 mag. We do not find counterparts to the two very large and bright UCDs in Fornax and Virgo with M_V=-13.5 mag, possibly due to survey incompleteness. The compact objects distribution in magnitude and space is consistent with that of the GC population. Their kinematics and spatial distribution associate them to the central galaxies rather than to the overall cluster potential. The compact objects have a mean metallicity consistent with that of the metal-rich globular cluster sub-population. Compact objects with high S/N spectra exhibit solar [alpha/Fe] abundances, consistent with typical dwarf elliptical galaxy values and unlike galactic bulge globular clusters. HST based size estimates for a sub-sample of eight compact objects reveal the existence of one very large object with half-light radius r_h around 30 pc, having M_V=-11.6 mag (~10^7 M_sun). This source shows super-solar [alpha/Fe] abundances. Seven further sources are only marginally larger than typical GCs with r_h in the range 4 to 10 pc. Conclusions: We consider the largest compact object found to be the only bona-fide UCD detected in our study. In order to improve our understanding of UCDs in Centaurus, a significant increase of our survey completeness is necessary.
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