The center fielder must take control if he is certain he has the ball, especially if he is right under it.
The etiquette is, if CF calls the ball first, it’s his. If RF calls it first and CF says nothing, it’s RF. If RF calls it first then CF calls it, RF has a choice of yielding, or reaffirming a second time “I’m on it!”, meaning, he is basically right under the ball right then which, if he is, he should be allowed to catch it. Then, if CF calls it a second time over RF, RF must peel away even if he is under it, moving to his left to avoid the collision. But really, if RF calls it, CF calls it, and RF reaffirms, then CF really should peel off at that point. There should not be a big ****-waving fight over the fly ball.
Am I making sense?