When should kid stop going to pediatrician?

Depends. On pediatricians. Some go from birth to 18 or 21. Some won't see kids that become pregnant as they will need an obstetrician. Always best to ask your pediatrician their policy, so you won't be surprised.
Pediatric age. Pediatricians take care of children from birth until they are 21 years old. In the past, most parents transferred their 18-year-olds to a family physician or internist. Nowadays, more and more children stay with their pediatricians. In essence, a newborn baby and a senior in college can actually meet at the pediatirician's office!
Kids choice. There is a natural pattern that kids seem to follow. I will seek kids from birth to 18.However,for some leaving lasts a few extra years and some migrate out as soon as they berate their parents enough for taking them to a "baby doctor".I figure any kid over 8 or so should begin to make decisions about their health.