Tarellian starships (also referred to as Tarellian plague ships) were vessels used as late as the 2360s to carry Tarellian refugees, following the Tarellian Civil War. These ships were equipped with warp drive and transporter technology.
Nearly every star system that the vessels entered either turned them away or destroyed them, through fear of spreading the Tarellian plague. By the early 2360s, there was only one of these ships known to still exist.
In 2364, the USS Enterprise-D encountered the last surviving vessel, and its sparse crew. On board the Enterprise-D at the time, Wyatt Miller joined the last of the Tarellian crew, hoping that he would, some day, find a cure for their plague. (TNG: "Haven")
According to the script, this vessel was described as "a ship of strange, unearthly design. Its center is a shiny globe. Dozens of spike-like structures jut out of it, tumbling end over end as the vessel moves along. Though clearly alien, there is a pleasing aesthetic quality to the ship, which gives off a soft, violet glow." Furthermore, according to the script, this ship was built at a base located three miles below sea-level.
For more information on this design and history of this model, please see: Studio models.