Only you can use abilities of cards in graveyards. For example, if a spell requires that you exile cards from your graveyard, you can exile cards from any graveyard. Any card that looks at cards in graveyards looks at any or all your graveyards.

Cards owned by your opponents still go to the appropriate graveyard.

If an effect asks how many cards are in your graveyard, use the total number of cards in all your graveyards. However, they are still separate graveyards. If an effect affects a single graveyard, such as shuffling it into its owner’s library, only that one graveyard is shuffled in.

Speaking of that, cards in graveyards are shuffled into their owners’ libraries. You won’t put any cards from graveyards you stole, er . . . borrowed into your library.

If more than one player controls a Graveyard Busybody, the one that entered the battlefield most recently “wins.” The controller of that Graveyard Busybody has all the graveyards, and any other player’s Graveyard Busybody is a 0/0 that is put into the graveyard that player used to have as a state-based action.