(This question could probably be made better if someone answers What time does a bar mitzvah come into effect?, but for now i'll just use the earlier or later time, as applicable.)
Let's say a boy's Hebrew birthday is tonight, and he's turning 13 (bar mitzvah). This afternoon, before shkia (the boy is definitely 12), the family (2 adult men plus the bar mitzvah boy) sits down to have a meal with bread. The meal goes on until after tzeit, and so the boy is definitely 13. Can he join in the zimun? What about lead it?
This question is obviously only according to those that do not l'chatchila include a 12-year-old for a zimun.
FWIW, when we potentially had this case, we just pushed off supper until after tzeit to avoid the problem.