  Systematic studies have revealed hundreds of ultra-compact dwarf galaxies
(UCDs) in the nearby Universe. With half-light radii $r_h$ of approximately
10-100 parsecs and stellar masses $M_*$ $\approx$ $10^6-10^8$ solar masses,
UCDs are among the densest known stellar systems. Although similar in
appearance to massive globular clusters, the detection of extended stellar
envelopes, complex star formation histories, elevated mass-to-light ratio, and
supermassive black holes suggest that some UCDs are remnant nuclear star
clusters of tidally-stripped dwarf galaxies, or even ancient compact galaxies.
However, only a few objects have been found in the transient stage of tidal
stripping, and this assumed evolutionary path has never been fully traced by
observations. Here we show that 106 galaxies in the Virgo cluster have
morphologies that are intermediate between normal, nucleated dwarf galaxies and
single-component UCDs, revealing a continuum that fully maps this morphological
transition, and fills the `size gap' between star clusters and galaxies. Their
spatial distribution and redder color are also consistent with stripped
satellite galaxies on their first few pericentric passages around massive
galaxies. The `ultra-diffuse' tidal features around several of these galaxies
directly show how UCDs are forming through tidal stripping, and that this
evolutionary path can include an early phase as a nucleated ultra-diffuse
galaxy (UDG). These UCDs represent substantial visible fossil remnants of
ancient dwarf galaxies in galaxy clusters, and more low-mass remnants probably
remain to be found.
