Just sent my 11-year old son ORD to SJU on AA... they charge $30 for escorting him on / off the plane but did not look after him while on the flight.
His 11-year old friend flew SJU to ORD two weeks ago and reported the same experience.
Basically, the AA $30 fee covers escorting the minor on / off the plane. I would assume that this would cover those who connect at a hub, too (but that is my assumption). There is no on-board extra attention (at least that is what the gate agents insist and demonstrated by the kids' experience).
The fee is optional... if you don't pay the fee, the minor can walk off the plane like anyone else. My concern with this is even though he was on a direct flight, what happens if his plane is re-routed somewhere on an emergency and they deplane? I personally want someone "official" to look after him in my absence.
That's my AA experience...