  We investigate the properties of long tidal tails using the largest to date
sample of 461 merging galaxies with $\log(M_\ast/\rm M_\odot)\geq9.5$ within
$0.2 \leq z \leq 1$ from the COSMOS survey in combination with {\it Hubble
Space Telescope} imaging data. Long tidal tails can be briefly divided into
three shape types: straight (41\,per\,cent), curved (47\,per\,cent) and plume
(12\,per\,cent). Their host galaxies are mostly at late stages of merging,
although 31\,per\,cent are galaxy pairs with projected separations $d>20$\,kpc.
The high formation rate of straight tidal tails needs to be understood as the
projection of curved tidal tails accounts for only a small fraction of the
straight tails. We identify 165 tidal dwarf galaxies (TDGs), yielding a TDG
production rate of 0.36 per merger. Combined with a galaxy merger fraction and
a TDG survival rate from the literature, we estimate that $\sim$\,5\,per\,cent
of local dwarf galaxies are of tidal origin, suggesting the tidal formation is
not an important formation channel for the dwarf galaxies. More than half of
TDGs are located at the tip of their host tails. These TDGs have stellar masses
in the range of $7.5\leq\log (M_\ast/\rm M_\odot)\leq9.5$ and appear compact
with half-light radii following the $M_\ast$ - $R_{\rm e}$ relation of low-mass
elliptical galaxies. However, their surface brightness profiles are generally
flatter than those of local disc galaxies. Only 10 out of 165 TDGs have
effective radii larger than 1.5 kpc and would qualify as unusually bright
ultra-diffuse galaxies.

Astrophysics of Galaxies