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In a scenario where Alexander or his generals conquer most if not all of Arabia and is ruled by one of the Diadochi (and their descendants), how likely is it for a Hellenic Arabia to end up falling under Roman, Persia or even Aksumite rule?

Or would a Hellenic Arabia hold the distinction of being of the few (if not only) Diadochi descended dynasty that avoids Roman (or other) conquest for a significant period of time?
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