Results. For 94% of the sources included in the masks, we measure successfully a redshift. Because of 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. For one of these targets HST WFPC2 imaging is available, yielding a size estimate of r(n) less than or similar to 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) less than or similar to 70 pc. Hence our survey confirms the extreme rarity of massive UCDs. We find that the radial distributions of Centaurus and Fornax UCDs with respect to their host clusters' centres agree within the 2 sigma level.