Q. Why is my kitty going outside the litter box?
A. First, it is important to determine if it is the result of spraying or inappropriate urination. Spraying is a result of kittens marking their territory, and is generally just a splatter, whereas inappropriate urination will be a larger puddle. You will want to address any urination outside of the litter box quickly, before it becomes normal behavior for your kitten.
If your kitten is spraying, try making her feel more secure, as that is often why cats get possessive. If inappropriate urination has become an issue with your kitten, the most important thing you can do is make an appointment with your veterinarian. He or she will perform a physical exam and urinalysis to determine if the problem is medical. If it isn't, seek advice from a veterinary behaviorist.