I used to carry a 61,000mAh battery for my Mac that I have brought onto aircraft.

Last time I was flagged down and told it's too big, but since I couldn't just leave it, they let me pass saying I can't fly with this next time. I have since kept this at home. I don't think it has changed since I recently asked, but the limit is quite high. Definitely more than 8000mAh.