I've established a small base on an island where wolves and cats do not spawn. If I want to tame a wolf I'll need to take a boat on a long journey to a forest and wait one to spawn. I could load my soon-to-be-tamed-wolf in a boat, but that would mean I'd have to make another long trip if I wanted a second pet.
Normally, when I do this I'd feel comfortable swimming or walking back to my house because it's so close but this excursion is large enough I'd want to rely on the teleporting mechanics to make it easier.
How far away can I get from a tamed pet before it stops teleporting to me? Will the wolf, who can't swim as the fast as I can operate the boat, teleport to me when I return to my island?