Context : We recently initiated a search for ultra-compact dwarf galaxies ( UCDs ) in the Centaurus galaxy cluster ( Mieske et al . 2007 ) , resulting in the discovery of 27 compact objects with -12.2 < M _ { V } < -10.9 mag . Our overall survey completeness was 15-20 % within 120 kpc projected clustercentric distance . Aims : In order to better constrain the luminosity distribution of the brightest UCDs in Centaurus , we continue our search by substantially improving our survey completeness specifically in the regime M _ { V } < -12 mag ( V _ { 0 } < 22.3 mag ) . Methods : Using VIMOS at the VLT , we obtain low-resolution spectra of 400 compact objects with 19.3 < V _ { 0 } < 21.3 mag ( -14 < M _ { V } < -12 mag at the Centaurus distance ) in the central 25 ^ { \prime } of the Centaurus cluster , which corresponds to a projected radius of \sim 150 kpc . Our survey yields complete area coverage within \sim 120 kpc . Results : For 94 % of the sources included in the masks we successfully measure a redshift . Due to incompleteness in the slit assignment , our final completeness in the area surveyed is 52 % . Among our targets we find three new UCDs in the magnitude range -12.2 < M _ { V } < -12 mag , hence at the faint limit of our survey . One of them is covered by archival HST WFPC2 imaging , yielding a size estimate of r _ { h } \lesssim 8-9 pc . At 95 % confidence we can reject the hypothesis that in the area surveyed there are more than 2 massive UCDs with M _ { V } < -12.2 mag and r _ { eff } \lesssim 70 pc . Our survey hence confirms the extreme rareness of massive UCDs . We find that the radial distributions of Centaurus and Fornax UCDs with respect to their host clusters ’ centers agree within the 2 \sigma level . Conclusions :