I don't know if there are specific terms that are required for a doctor to refuse to take on a patient, but I have personally dealt with this kind of situation. When I was nearly 9 months pregnant with my fourth baby, I was in a situation where I needed to find a new OB and had a heck of a time finding an OB to take me on at that point in my pregnancy. They all considered me too high risk since they hadn't been there with me throughout my prenatal care. Finally, when I was nearly about to deliver, a friend of a friend took me on as her patient and I was totally grateful. I don't know what would have happened to me or my youngest daughter if she hadn't taken me on and agreed to do my C-section. That was one of the most stressful experiences.