Updated December 14, 2020
because so many more chondrichthyes and chimaera have been added to the LRT.

You might think these two flat bottom dwelling fish
were outliers, weird-ohs and anomolies. Not so! They were key players!
The taxonomic addition of Thelodus and Squatina
shifts sharks, ratfish and sturgeons to a node prior to the placoderm, Entelognathus, in the large reptile tree (LRT, 1470 taxa). The extant Squatina (angelshark) remains remarkably similar to its sister in the LRT, the Early Silurian Thelodus (Fig. 1) despite the 435 million year difference in appearance.
The basal taxon of any cladogram
is potentially the trickiest node, the one fraught with the most possible error. The choice (and it is a choice made by the clade maker) is vitally important. The software assumes this is indeed THE ancestral taxon. So it better be a valid ancestral taxon.

Thelodus parvidens (Agassiz 1839; Early Silurian; 5–15cm in length) is the basalmost taxon in the LRT because it just barely shows skull bones. This jawless toothless(?) bottom feeder gave rise to sharks, like Squatina, and placoderms, like Entelognathus, which gave rise to bony fish and tetrapods, like humans.

Squatina oculata (Bonaparte 1840) is the extant smoothback angelshark, a bottom feeder sister to Thelodus and the basalmost tested shark. The gill arches are transformed to jaws with teeth. The general morphology is little changed from the Early Silurian and informs the genesis of many vertebrate traits.

Ferrón and Botella 2017 wrote:
“Thelodonts are an enigmatic group of Paleozoic jawless vertebrates that have been well studied from taxonomical, biostratigraphic and paleogeographic points of view, although our knowledge of their ecology and mode of life is still scant. Their bodies were covered by micrometric scales whose morphology, histology and the developmental process are extremely similar to those of extant sharks.”
“Currently, there are 147 described thelodont species, belonging to 54 different genera and grouped in six orders (Sandiviiformes, Loganelliiformes, Shieliiformes, Phlebolepidiformes, Thelodontiformes and Furcacaudiformes). Only 29 of these species are known from articulated specimens, which provide the information about the general aspect and some anatomical features of thelodonts. The remaining 118 species are described only on the basis of associations of (or a few) disarticulated scales.”
By the way
this further separates sharks from ‘spiny shark’ acanthodians, which nest with Cheirolepis and Brachyacanthus in the LRT.

And once again,
we have living specimens little changed from deep time ancestors from our own family tree. These new taxa document the origin of jaws and teeth, bottom feeding, a flattened overall morphology, broad fins in contact with the substrate more useful for propulsion than the tail and the origin of the internal and external skeleton.
The hypothesis of relationships that nests Thelodus with Squatina
appears to be novel. A Google search failed to find any similar prior citation. If anyone can alert me to an earlier reference, then we’ll consider this independent discovery a confirmation of that earlier hypothesis.
References
Agassiz L 1839. Fishes of the Old Red Sandstone. In Merchison’s Silurian System. Künstliche Steikerne von Konchylien und Fische. Neues Jahrbuch Mineralogie.
Bonaparte CL 1840. Iconografia della fauna italica per le quattro classi degli animali vertebrati. Rome.
Ferrón HG and Botella H 2017. Squamation and ecology of thelodonts. PLoS One. 2017; 12(2): e0172781.
Zhu M, Yu X-B, Ahlberg PE, Choo B and 8 others 2013. A Silurian placoderm with osteichthyan-like marginal jaw bones. Nature. 502:188–193.
wiki/Entelognathus
wiki/Theodus
wiki/Squatina
wiki/Smoothback Angelshark