Not quite practicing yet (currently in fellowship, but am a board-certified residency grad). In my residency (military), we routinely saw patient up to age 23 as long as they were still covered by their parents insurance (Tricare). In general, pediatricians seem to top out at age 21 to 23. It is interesting that certain pediatric subspecialties will see adults as well: pediatric hematology/oncology will often be the treating physicians for people in their 20s that have ALL or some lymphomas since they have more experience with these disease processes specifically in younger people (physiologically, most people in their 20s are more like teenagers than they are like the older adults that internists see more often). Pediatric pulmonologists may see some younger adults with cystic fibrosis if they are in a place where there isn't a good transitioning set-up. In my particular field (cardiology) we probably see the most adults. Statistically, adult congenital heart disease is dealt with by pediatric cardiologists far more often than adult cardiologists (however, there is a great need for adult cardiologists to become more involved and more savvy to adult congenital). The oldest patient in our enpanelment is in their 60s. I have seen a 52-year-old in clinic and recently was in the Pediatric Cath Lab with a 44-year-old.
Pediatricians should be savvy to transitioning their patients to adult care. This is especially important for children with chronic diseases. Insurance issues should be thought about well in advance especially with the latter group.