We present a novel approach to constrain the formation channels of Ultra-Compact Dwarf Galaxies ( UCDs ) . They most probably are an inhomogeneous class of objects , composed of remnants of tidally stripped dwarf elliptical galaxies and star clusters that occupy the high mass end of the globular cluster luminosity function . We use three methods to unravel their nature : 1 ) we analysed their surface brightness profiles , 2 ) we carried out a direct search for tidal features around UCDs and 3 ) we compared the spatial distribution of GCs and UCDs in the halo of their host galaxy . Based on FORS2 observations under excellent seeing conditions , we have studied the detailed structural composition of a large sample of 97 UCDs in the halo of NGC 1399 , the central galaxy of the Fornax cluster , by analysing their surface brightness profiles . We found that 13 of the UCDs were resolved above the resolution limit of 23 pc and we derived their structural parameters fitting a single Sérsic function . When decomposing their profiles into composite King and Sérsic profiles , we find evidence for faint stellar envelopes at \mu = \sim 26 mag arcsec ^ { -2 } surrounding the UCDs up to an extension of 90 pc in radius . We also show new evidence for faint asymmetric structures and tidal tail-like features surrounding several of these UCDs , a possible tracer of their origin and assembly history within their host galaxy halos . In particular , we present evidence for the first discovery of a significant tidal tail with an extension of \sim 350 pc around UCD-FORS 2 . Finally , we studied the local overdensities in the spatial distribution of globular clusters within the halo of NGC 1399 out to 110 kpc , to see if they are related to the positions of the UCDs . We found a local overabundance of globular clusters on a scale of \leq 1 kpc around UCDs , when we compare it to the distribution of globulars from the host galaxy . This effect is strongest for the metal-poor blue GCs . We discuss how likely it is that these clustered globulars were originally associated with the UCD , either as globular cluster systems of a nucleated dwarf galaxy that was stripped down to its nucleus , or as a surviving member of a merged super star cluster complex .