Destroyed monsters go to the graveyard, including destroyed Fusion or Synchro monsters.
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Synchro Monsters are placed in the Extra Deck along with the Fusion Monsters at the beginning of a Duel.
Monsters considered destroyed by battle cannot return themselves from the field to hand or deck. If Fiber Jar was considered destroyed by battle, it will not shuffle itself back into deck even though its on the field while the effect resolves. After resolution, it will go to the graveyard.
Destroyed or tributed Fusion Monsters go to the graveyard. They will return to the Extra Deck if something tries to return them to hand or deck.
No, the Crystal Beast goes to the graveyard if tributed. Crystal Beasts only get to choose to go to the S/T zone if they are 'destroyed'. Tributing, or 'sending', are not destruction effects. Effects that destroy will say so on the card, and also monsters can be destroyed by battle.
Just like regular monsters, Fusion monsters will go to the Graveyard if they are destoyed. If a Fusion monster is supposed to "return to the owner's hand" or "return to the owner's deck" because of a card effect, it is returned to the Extra/ Fusion Deck.