I think he’s marking. I had a similar problem with my bun Yohio before he was neutered, but neutered buns can mark too if they like. In Yohio’s case it was solved by placing the box in a corner, on a pee pad and with a mirror behind the box. It doesn’t nned to be a mirror of course, just something non-absorbent and non-chewable, something that can be wiped off easily. Yohio did exactly like your bun does – backed up, extended his tail outside the box and peed like three feet up the wall. He wasn’t a big bun, so I was quite impressed.

I’ve never tried a hooded cat box for my buns, but it might work.

For my Bam I have litterboxes with a detachable “lid” – they do keep stuff in better than a box without a lid:

Some rabbits are very picky with their litter boxes. My bunnies did this whenever their litter box was too small. Got them an XXL cat litter box and have not had that problem since

That seems more like he’s unaware it’s not in the litter box. He thinks he’s doing it right because he’s in the box, he just doesn’t understand the way his urine exits in an arch which will jump the lip. While we say rabbits are litter boxed trained, with low-lip boxes, I think it becomes more apparent that rabbits understand the concept of “Go pee/poo in this box”, but not the other item which is “The pee/poo should go in the box”. It’s like a rabbit pooping, but jumping out of the litter box pre-maturely, so the poo flings outside or ends up exiting the bum once the rabbit’s outside.

High walls would help. This is Wick’s litter box, which has a low lip, but I put a panel on it because he kept peeing over it: http://www.instagram.com/p/BXsXo28FTcG/?taken-by=wick_theboogeyman

My rabbit does the same thing. I think he’s usually telling me he wants me to clean his box because as soon as I clean it, he stops

My rabbit does this and I solved the issue with a high sided litter box. This way when he backs up it is just on the wall of the box rather than anywhere else. They sell litter boxes with high sides as well as a storage bin