If the bean runs in the context of the caller's tx (required, mandatory and supports), the tx will be rolledback. If the bean runs in unspecified tx (NotSupported, Never and Supports), the tx is NOT automatically rolledback.
Now, what happens when the bean runs with "supports" attribute (support comes in both the above cases) ... will be tx be rolledback or not ???
It all depend's if the method was called in a transaction context, if the caller of the bean call's a method that was marked as Supports and there is a transaction, then that transaction will be propagated to the next call, like a chain, so in the case of:
in such a case, the Bean C has a transaction Context that comes form Bean A, so, the transaction can be rollback