Bumping this because I want to comment, follow it, and draw attention back to it because I think it's wicked
Other than
possibly adrena-frogs, this looks like a fantastic card. Personally I'd name it "Regeneration" much like momentum is a status given by "Momentum", but more importantly...
This on adrena-frogs would be very dangerous, but the frog would still be a soft target for CC. It would however, even if it was killed the next turn, heal 20HP (equal to a Heal) before the opponent even has a turn. In this sense, it may overshadow Heal. But that is putting one's eggs into one basket. The deck would still bomb vs DR Shields and Fire Shield (unless you wanted to give the card's healing power to the enemy to Lobotomize it).
Question: by "lobotomizing" permanents would they stay on the field even after they're supposed to sacrifice automatically? If you remove Sundial, Phase Shield or Bone Wall's abilities then they have no conditions to destroy themselves — so they would continue Regenerating?
I agree that in certain ways this is better than Liquid Shadow, but LS can also be an effective CC (for example, against a Lava Golem). More questionably, Rejuvenation has the ability to Lobotomize permanents in a unique way—PC that Life could really come to appreciate. But this is balanced by giving the opponent the Regeneration ability.
Hm, to reiterate, I think it should be called Regeneration