‘Horny’ Falcatus enters the LRT

Not many fossils are fossilized while mating or courting.
And not many have an ‘antler’. Today’s ‘antler’ (Figs. 1-3) is found on Falcatus, an extinct ratfish, according to both traditional studies and the large reptile tree (LRT, 1495 taxa).

Distinct from Chimaera
Falcatus has a jaw joint far behind the orbit, as in sharks, not below the orbit as in Chimaera (Fig. 4). Falcatus also has a shark-like tail fin, not the long straight streamer found in Chimaera. 

Lund 1985 considered Falcatus
to be a member of the clade Cladodontida (later a junior synonym of Symmoriida) and a member of the family Stethacanthidae. Here with far fewer tested taxa Falcatus nests with Chimaera, the ratfish (Fig. 4).

Several hundred million years have passed
since Falcatus in the Mississippian (Early Carboniferous) to the present day, plenty of time for the propulsion system to shift from the tail to the pectoral fins.

References
Lund R 1985. The morphology of Falcatus falcatus (St. John and Worthen) a Mississippian stethacanthid chondrichthyan from the Bear Gulch limestone of Montana. Journal of Vertebrate Paleontology 5:1–19.
St. John OH and Worthen AH 1883. Description of fossil fishes: a partial revision of tehe Cochliodonts and Pasmmodonts. Geological Survey of Illiniois 7:55–264.

wiki/Symmoriida
wiki/Falcatus