Tarquin's species were a humanoid spacefaring race from an unnamed planet in the Delphic Expanse. They had multiple antennae sprouting from their heads, and yellowish-brown skin. They were extremely long-lived; one member of their species claimed to be over four hundred years old. About one in every fifty million people of this race were born with telepathic abilities. Telepaths were seen as a threat to the rest of the population, and were therefore exiled off-world. (ENT: "Exile")
It was never explicitly said that their homeworld is located in the Delphic Expanse, though its location given as thirty light years from Tarquin's planet makes this likely.