You've asked very similar question at least three times. The domain is always the same: sport teams, leagues and players but the details you provide are always different and this is why you get and accept different answers. You clearly in the state of analysis paralysis. There is very little chance that you would come up with the perfect model the first time. Start writing code and tests and you will get immediate feedback. Look for code smells, refactor and a better model will emerge.
Regarding this version of the question. Aggregate definition:
A cluster of associated objects that are treated as a unit for the
purpose of data changes. External references are restricted to one
member of the Aggregate, designated as the root. A set of consistency
rules applies within the Aggregate's boundaries.
And the classic example is Order as Aggregate root and Order Lines as Entities that are part of the Order Aggregate. Note that Order Lines do not make sense outside of the Order.
In your case the rule that "team cannot exist without a league" is different. It is not enough to proclaim Team to be a part of League Aggregate. It is similar to "Order can not exist without a Customer". It does not mean that the Customer is part of the Order Aggregate. Customer is its own Aggregate, it makes sense on its own. Just like the Team makes sense on its own, it has its own history, fans etc.
This problem can also be approached from 'data-exchange' stand point. In Evan's example the whole Order gets locked so that internal invariants can be enforced. If you make changes to the League would you also want all Teams and Players to be locked as well?
So based on the information you provided this time you need two Aggregates: League and Team. Keep in mind that Aggregates can reference each other.
