We got Asher back in August.  He was always  good at going in his liter, the typical poop markings here and there, but never peeing outside of it.  When we first got him he’d go pee in his liter only.  After about a month he would pee and poop in same spot, outside of, but right near his liter box, on our metal grates for our forced AC/Heat(pretty sure they seemed like the grates in his liter box).  We blocked these grates off and he stopped for a little while, but recently he started to poop and pee (ALOT) on the rug in front of the grates instead (essentially the same spot) BUT NEVER does this anywhere else in our living room where he has free range).  We do have two cats that Asher gets along with very well.  I feel that he does go the bathroom outside liter box more at night when cats are around…. I figured that pooping was territorial due to the cats, but I can’t handle the peeing!!!!  If they pee once in a spot does the smell make them continue. to do so in that same spot?  I know a couple of the accidents weren’t caught/cleaned (ick I know!) so the scent was definitely still present.  1) if so what is used to remove odor for accidents on rugs/floors?  2). could this be territorial?  3). Will neutering help? (he has vet apt for consult Friday morning)  
We had to throw away rug.. that’s how bad it was… luckily it was an area rug that was due for updating, but I am hesitant to buy a new one until we figure this bunny out!!!  Any advise would be appreciated
*also sorry if this was already a post, the search button was not working until page was updated and I need answered ASAP!!!*
Thank you