These lovely, graceful beasts of another age left no living descendants. However, some critter (or clade) has to be its closest surviving relative. I’ve read in various places that it’s not known for sure. Some suggest other hooved animals, and one place brought up the intriguing possibility that its closest surviving relative might be. . . the rabbit! (While it may or may not be true, it’s not implausible out of hand considering the elephant/hyrax relationship.)
Anyway. . . the GQ is “Is there any closer consensus on who’s next of kin–and what evidence was used to determine that?”
Damn, that thing is strange. Like “George Lucas re-invents the rhino”
Most sources I’ve seen place them within the Ungulata, with their closest relatives possibly being the Altungulata (aka Paenungulata, depending on who you ask). And, within that group, the surviving members are horses, elephants and rhinos (along with hyraxes and members of Sirenia - dugongs, sea cows and such). Which would mean that their closest living relatives are probably just who they look like they should be related to.
Unfortunately, there isn’t clear evidence which indicates just where on a mammalian cladogram they fall (their lineage is usually connected with a “?”, as shown here - they’re found within Dinocerata).