We have obtained high-resolution spectra of 23 ultra-compact dwarf galaxies (UCDs) in the Fornax cluster with -10.4>M_V>-13.5 mag (10^6<M/M_*<10^8), using FLAMES/Giraffe at the VLT. This is the largest homogeneous data set of UCD internal dynamics assembled to date. We derive dynamical M/L ratios for 15 UCDs covered by HST imaging. In the M_V-sigma plane, UCDs with M_V<-12 mag are consistent with the extrapolated Faber-Jackson relation for luminous ellipticals, while fainter UCDs are closer to the extrapolated globular cluster (GC) relation. At a given metallicity, Fornax UCDs have on average 30-40% lower M/L ratios than Virgo UCDs, suggesting possible differences in age or dark matter content between Fornax and Virgo UCDs. For our sample of Fornax UCDs we find no significant correlation between M/L ratio and mass. We combine our data with available M/L ratio measurements of compact stellar systems with 10^4<M/M_*<10^8, and normalise all M/L estimates to solar metallicity. We find that UCDs (M > 2*10^6 M_*) have M/L ratios twice as large as GCs (M < 2*10^6 M_*). We show that stellar population models tend to under-predict dynamical M/L ratios of UCDs and over-predict those of GCs. Considering the scaling relations of stellar spheroids, UCDs align well along the Fundamental Manifold, constituting the small-scale end of the galaxy sequence. The alignment for UCDs is especially clear for r_e >~ 7 pc, which corresponds to dynamical relaxation times that exceed a Hubble time. In contrast, GCs exhibit a broader scatter and do not appear to align along the manifold. We argue that UCDs are the smallest dynamically un-relaxed stellar systems, with M > 2*10^6 M_* and 7<r_e<100 pc. Future studies should aim at explaining the elevated M/L ratios of UCDs and the environmental dependence of their properties.
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