The HST/ACS Coma Cluster Survey. X. Nuclear star clusters in low-mass
  early-type galaxies: scaling relations
  We present scaling relations between structural properties of nuclear star
clusters and their host galaxies for a sample of early-type dwarf galaxies
observed as part of the Hubble Space Telescope (HST) Advanced Camera for
Surveys (ACS) Coma Cluster Survey. We have analysed the light profiles of 200
early-type dwarf galaxies in the magnitude range $16.0 < m_{F814W} < 22.6 $
mag, corresponding to $-19.0 < M_{F814W} < -12.4 $ mag.
  Nuclear star clusters are detected in 80% of the galaxies, thus doubling the
sample of HST-observed early-type dwarf galaxies with nuclear star clusters.
\changed{We confirm that the} nuclear star cluster detection fraction decreases
strongly toward faint magnitudes. The luminosities of nuclear star clusters do
not scale linearly with host galaxy luminosity. A linear fit yields L$_{nuc}
\sim $L$_{gal}^{0.57\pm0.05}$. The nuclear star cluster-host galaxy luminosity
scaling relation for low-mass early-type dwarf galaxies is consistent with
formation by globular cluster accretion. We find that at similar luminosities,
galaxies with higher S\'ersic indices have slightly more luminous nuclear star
clusters. Rounder galaxies have on average more luminous clusters.
  Some of the nuclear star clusters are resolved, despite the distance of Coma.
We argue that the relation between nuclear star cluster mass and size is
consistent with both formation by globular cluster accretion and in situ
formation.
  Our data are consistent with GC inspiraling being the dominant mechanism at
low masses, although the observed trend with S\'ersic index suggests that in
situ star formation is an important second order effect.
