This only works if the Spiral Zetsu is the fruit of the God Tree.its just that him reaching out for yamato shows desperation. my theory on swirly is the same as yours. the fruit. we'll see
I would assume here that the fruit of the Shinju always requires a vessel in order to showcase it's full powers. It's like a separate entity (Evil) which was sealed by the Shinju (Good). Look up TBY's Sojobo theories if you want details.
In order to be free, the fruit tried to obtain a vessel. I suspect,
That the first Vessel was Kaguya.
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The Second vessel was Obito.
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The third was Yamato, Spiral abandons his vessel for unknown reasons (Yamato falls under Mugen Tsukuyomi making him useless as a vessel, about to become complete).
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Since, Spiral did not have a vessel, he was absorbed/sealed by the God Tree.
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He was clearly desperate for a vessel to prevent being absorbed/sealed.
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Sasuke, a direct descendant of Kaguya with the powers of Sharingan and Rinnesharingan/Rinnegan is the perfect Vessel for Spiral.
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