Are there rules anywhere clarifying which player's Discard Pile cards go into? eg.

(i) If I attach a card to an opponent's character and that charcetr is destroyed, into whose discard pile does the attcahed card go?

(ii) If I take control of an opponent's charcater "until the end of the phase" and that character is destroyed during the Phase, does it enter my or the opponent's Discard Pile? If mine, does it then move to Opponent's Discard Pile at the end of the Phase?

Thanks.

Discarded cards always go in to their owner's discard pile, and not their controller's discard pile. This is stated in the Core rules as follows:

Control and Ownership

Players “own” all cards that they brought to the game in their deck...

...

When a card leaves play (is moved to a player’s hand, deck, or discard pile), it is sent to the appropriate out of play area of its owner.

With regards to (ii) specifically, this is also re-stated in the FAQ as follows:

(1.13) Gaining Control

...

When you have taken control of a card, you are considered to be that card’s controller, but not its owner. When that card leaves play for any reason, or at the end of the game, you must return it to its owner. If it leaves play as the result of a game or card effect, it is returned to its owner’s control, but still is placed out of play. So, for example, if the card would be sent to a discard pile, it is placed in its owner’s discard pile.

...

Thanks. More clear Core rules I have failed to find despite looking! I can see how that makes for easier maintained seperation of Players; decks but it might make for richer gameplay if you could get opponent's cards into your discard pile.