The appendices state with clarity that Elessar and Arwen had at least one son. The heir was Ecthelion? Something like that. However, if you're proposing a what if...
The character of Aragorn would have disallowed the kind of choices that King Henry VIII and others in history made. That's just the way Tolkien drew him. IF, and I say IF he had had no heirs, he would probably have made the eldest son or daughter of Faramir and Eowyn his heir.
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