I scanned through all the three pages of this post. I saw all the cages and all the hutches. For about 11 years, my rabbit Bunny lived in our house. She never spent a moment in a cage or a hutch for these 11 years. She had perfect litter box manners. There were some chewing incidents in the beginning, and some pee marking incidents for the first 4 weeks she was turned loose in the house. well, Ok, Ok, some other incidents. We had a leather couch, maybe cost $1000 or more , and Bunny chewed a hole in it. We weren't upset, we just covered up the hole with a pillow!
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About Bunny's litter box behaviors. She really loved to go outside in her latter years and me or my wife would always be with her...never to leave her alone outside. After a 1/2 hour or so outside, we'd bring her inside and the first thing she often did was run to her litter box...I think that she would not poop or pee outside the house...only in her litter box...what absolute litter box training!.