Hercule in another dimension communicating with everyone on earth via TP is the best ft. It was King Kai... he made it possible that Vegeta can communicate to everyone on earth. Crazy thing is, he was in another dimension doing this. Heck, he even made it possible for Vegeta to speak to everyone in the universe.
In terms of "offensive" TP(ie. mental possession), then yeah, Babidi's is the best we've really seen. The only thing that tops it(in terms of "possession" or w/e) would be something like Ginyu's body-swap technique, but that's not really TP/psi at all -- it's more akin to what Deadman does. /shrug
If we're just talking general TP, however, then even the likes of King Kai can "broadcast" on a universal scale:
I would *assume* this ability comes with his status as a Kaio(like how all the Kaioshin can use KaiKai to teleport.) If so, every one of the Kaio should be capable of at least the same level of TP(likely far more if we're talking about the Dai Kaio or Kaioshin, given their greater cosmological ranks)... But TP just isn't something we've seen much of in DB.
Babidi's gimmick wasn't strictly TP, though. It was some form of esoteric magical possession that was further empowered by the rage/hate/anger of the individual he was possessing.
...And if Daima is any indication, the Demon Realm "Majin magic" that Babidi used is pretty much as powerful as magic gets in DB, so it makes sense why King Kai(or even Shin himself) had no direct counter for it. /shrug