My school separates adults and kids. The older kids who are bored with the kids' classes are invited on an individual basis to the adults' classes. Adults' class I'd 14 & up, but there's a few 13 year olds (and a 12 year old) who are good enough to be in with the adults. In sparring, we treat them the same as everyone - go at the lower rank/ability's limit. Don't make it easy, but don't make it impossible; let them keep up.
Kids have the same curriculum as adults, just a different pace. A kids' 1st dan is doing adults' advanced green belt/brown belt stuff (3rd kyu-2nd kyu). They test for adult rank after they turn 14 and when they've met the adult standards. So, when a kid black belt turns 14, he/she is progressively taught stuff to bring him/her to adult 1st dan level. Once they've shown they're ready to test, they test. Could be a few months, could be a few years (haven't seen it take years, but it's possible). If the kid is ready the learn the stuff before he/she's 14, they'll be taught it and test the first available test after they turn 14. They get tested when they're ready, not when a piece of paper says they're ready.
Most of us have been the only adult in class on quite a few occasions. By only adult, I mean real-world adult, not teenager. I just look at it as a class to slow down and concentrate on the little things. In sparring I try new things that I'd hesitate to try for the first time against my peers.
If being the only true adult in class was a consistent thing, I wouldn't stick around too long. One class I regularly go to had this happen. It became me and 6 kids (old enough to be in the adults' class). Had to change my schedule around to go on a different night where there's a dozen adults and all but one out rank me. It's a night and day difference.
Who's in class also depends on rank and how many students there are. If there's only 2 or 3 adult black belts, it's not easy to have an adult black belt only class. If you're the only adult green belt, it's not easy to have an adult green belt class. Me getting to the best class is tough because I'm 1 of only 4 non-black belt adults. Our school is about 75% actual adult black belts. The kids have an even mix of color belts (only 1 junior black belt).