Mosasauria: “The exact phylogenetic position of the clade containing mosasaurids and their closest relatives (aigialosaurids and dolichosaurs) within Squamata remains uncertain. Some cladistic analyses recovered them as the closest relatives of snakes, taking into account similarities in jaw and skull anatomies; however, this has been disputed[ and the morphological analysis conducted by Conrad (2008) recovered them as varanoids closely related to terrestrial monitor lizards instead. Longrich, Bhullar and Gauthier (2012) conducted a morphological analysis of squamate relationships using a modified version of the matrix from the analysis of Gauthier et al. (2012); they found the phylogenetic position of the clade containing mosasaurs and their closest relatives within Squamata to be highly unstable, with the clade “variously being recovered outside Scleroglossa (as in Gauthier et al., 2012) or alongside the limbless forms”.
the large reptile tree (LRT. 1006 taxa) nests the mosasaurs Tethysaurus and Tylosaurus with Aigialosaurus and this clade is a sister to the clade Saniwa + (Estesia + Varanus). All have a common ancestor that is a sister to Bahndwivici and Yabeinosaurus + Sakurasaurus. In other words, not close to snakes, earless monitors, Gila monsters or amphisbaenids.
Tylosaurus proriger (Marsh 1872, Late Cretaceous) was a giant mosasaur, a clade that traditionally and currently nests with small Aigialosaurus. Mosasaurs were sea-going giant varanoid lizards that gave live birth and had extra phalanges on the medial digits as the hands and feet were transformed into paddles. Large teeth appear on the pterygoids, but these are convergent with those found on basal marine snakes like Pachyrhachis. The nasals were fused together and fused to the premaxilla ascending process.
On a side note:
Caldwell 2012 asked, “What, if anything is a mosasaur?”
From the Caldwell abstract:
“This treatise critically assesses Camp’s  diagnostic characters for Anguimorpha, Platynota, Varanoidea, and Mosasauroidea, concluding that Camp’s data permit mosasaurs to be viewed only as anguimorphans, not platynotans nor varanoids. A similar critical assessment is given for the characters used to diagnose anguimorphans and varanoids in Estes et al. , concluding here that not a single character out of twenty-two is shared between varanoids and mosasaurs… It is concluded here that there is no character-based evidence to support phylogenetic hypotheses that mosasaurs are derived aquatic varanoid lizards. It is recognized that the concept and term “mosasaur” has ceased to exist in any biologically meaningful way, and that the future requires the construction of a new suite of terms and concepts to convey what we now think we know about these animals.”
The LRT agrees
with the above hypothesis (Fig. 4) to an extent. Mosasaurs and varanids shared a common ancestor, probably as early as the Permian. TA1045 (Rößler et al. 2012; yet unnamed) is one of the earliest known lepidosaurs. It lived during the Permian. Saniwa lived during the Eocene much later than the Cretaceous mosasaurs. I could not locate any Mesozoic varanids, though they were undoubtedly present.
On an another note
I just learned about this website: http://homepages.vodafone.co.nz/~jollyroger_wave/DinoNew/links2.htm
listing blogs and other web pages related to prehistoric topics. Both PterosaurHeresies and ReptileEvolution are listed. Thank you Vodphone/JollyRoger/DinoNews!
Caldwell M 2012. A challenge to categories: “What, if anything, is a mosasaur?” Bulletin de la Société Géologique de France 183(1): DOI: 10.2113/gssgfbull.183.1.7
Marsh OC 1872. Note on Rhinosaurus. American Journal of Science 4 (20):147.
Rößler R, Zierold T, Feng Z, Kretzschmar R, Merbitz M, Annacker V and Schneider JW 2012. A snapshot of an early Permian ecosystem preserved by explosive volcanism: New results from the Chemnitz Petrified Forest, Germany. PALAIOS, 2012, v. 27, p. 814–834