Fossils of T. arcuatus, the type and only species, including fin spines have been found in Scotland.

[3] Unlike other chondrichthyans that have three basal plates on pectoral fin (propterygium, mesopterygium and metapterygium), its pectoral fin had only two basal plates and lacked mesopterygium.

[4] Even through it is one of the earliest known stem-elasmobranchs, it is estimated to be a specialized suction feeding benthic predator, either ambushing or using stealth to approach its prey.

[5] While historically considered a hybodont, a 2016 study considered it to be a basal euselachian, with hybodonts more closely related to Neoselachii (the group of modern sharks and rays) than to Tristychius.

[6] Holocephali (chimaeras and relatives) Acronemus Tristychius Hybodontiformes (hybodonts) Neoselachii (modern sharks and rays)