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Outrigger is the term used here.
I believe "verge" rafter is the most architecturally correct (AC?) term for that rafter out on the edge. It is sometimes called a "varge" rafter, which suggests a corruption from verge to varge and thence to barge. Barges, having no roofs, have no rafters.
Similarly, furring strips were once called fairing strips. And now frieze blocks are being referred to as freeze blocks, or even freezer blocks.
But that's how language evolves. No "correct" name for a thing, just current usage. (Any fans of S.I. Hayakawa out there?)