Bab, that seems to be a common hitchhiker on live rock, and you're right, it is definitely an anemone. I have one that I've had for years. They are very sticky and seem to like to live in a cave in the liverock. I actually feed mine every once in a while and it eagerly snatches whatever food I offer it. Mine measures about two inches from tip-to-tip. It has slowly grown over the years. It never moves. I have it where it can't touch anything else as I think it would be damaging to whatever it comes in contact with. I have no idea what species it is, but it does appear to be related to the OP pic.