Hail to the King grants all 3 Ultimate Death spells, it appears.
I belive it might bear to mention that Hail to the King also grants access to Grimoire spells. Namely Rapture, which currently stands as the single most powerful AoE spell that can be spammed. I think removing the Grimoire spells from Hail to the King wouldn’t serve as much of a nerf, as the Lich King is still an insanely powerful creature without them and has easy access to a large variety of other AoEs, and that it would promote the Grimoires a bit more as individually uniqye creatures.
Also, Arena creatures and non-Grimoire enemies still have a tendency to spawn with Grimoire spells and it does feel a bit off. Especially since you can somehow get Grimoire spells in gems post-TotG.