Chimaera monstrosa (Linneaus 1758), the extant rabbitfish, a type of ratfish, nests between sharks and sturgeons in the LRT. The quadrate shifts anteriorly to below the orbit. The teeth are transformed and fused to plates and beaks. The large pectoral fins provide propulsion while the tail is reduced.
Heterodontus francisi (Girard 1855; 1m) is the extant horn shark. Here it is more closely related to the ratfish, Chimaera (above) than to sharks like Isurus. Not sure why this was never noticed before, except for the fact that no operculum is present over the 5 gill slits (a shark trait). The jaw joint is below the orbit. The nares open anteroventrally. The teeth are flat plates. Heterodontus swims using its pectoral fins, like skates, rays and ratfish.
Girard CF 1855. Characteristics of some cartilaginous fishes of the Pacific coast of North America. Proceedings of the Academy of Natural Sciences of Philadelphia, 7: 196–197.
Linnaeus C 1758. Systema naturæ per regna tria naturæ, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis. Tomus I. Editio decima, reformata.