Hi,
Thanks for asking your question on Just Answer. Congratulations on a new kitten. Diarrhea is not behavioral. Since your cat came from a shelter and it is a young cat, it is likely that it has parasites or is having diarrhea due to the stress of a new home or a diet change. In any case, it is important that you take your cat to the vet for a fecal examination to make sure that there are no intestinal parasites. Your kitten should be urinating in the litterbox. If not, this is cause for concern. Usually, kittens who are urinating outside the box have urinary tract infections. Sometimes, it's behavioral....but I would rule out underlying medical causes before concluding this is behavioral.
I hope this is helpful -- see your vet for a checkup and a fecal exam. It would be time and money well spent.
Please let me know if you need more information.
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