Sources for a Pshetel on the topic a kattan washed and ate a seudah and became a gadol during the seudah

Question

I am trying to work with my son on his Pshetel on the topic: If a 12 year old boy washed for a seudah and during the seduah it became night and now the boy is 13 and is a gadol, may he lead the bentching as part of a "mezuman"? We need some sources for an analysis of this question: What is the chiyuv of a katan vs. a gadol; is this similar to the question of yaaleh vyavo when rosh chodesh occurs during a seudah or is it different because here we are talking about a change in the person, not the zman, etc. etc.