Without ultimate control, there is no free will; however, what does the Theravāda (orthodox) tradition of Buddhism state about causality, determinism, or, i.e., fate?
No, nothing gets transferred at all.
Memories (even if not remembering, but the potential to remember), ignorance, 5 faculties level, attainments, some personalities, kamma, etc does get transferred. According to observations from the suttas and past life evidence cases.
All of them are of course impermanent, conditioned and therefore not self.
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Buddha was a Hedonist. Am I wrong?
I would say you are wrong, yes. 
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I believe the Buddha was the ultimate Hedonist, as he desired to eradicate all suffering and succeeded.
I suppose it depends how you define hedonism. Usually it is about indulging in sense pleasures, so not something the Buddha’s do.
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