I play Revelation of the Spheres. It says: Reveal the top 5 cards of an opponent's deck. Put into play a character revealed this way under your control.

I now want to trigger Stalking Hound "After an opponent's character enters play due to a triggered effect..." Can I?

Does the Hound look at ownership or control? 

 Excellent question.  I would assume it checks ownership based on the language.  The apostrophe-s on "opponent's" indicates we are using the possessive form, which indicates ownership by traditional grammar rules in English.

It would be appropriate to say "I have taken control of my opponent's card." In such a case it is clear that "opponent's card" means "owned by the opponent", and control is a different type of status.

Of course this argument is from grammar, not rules, so it might be completely wrong!

I agree, excellent question.

However, I don't believe "opponent's" references ownership.

Anytime ownership is used instead of controller it specifically mentions "owner's" either in the effect itself or the rules. (or at least I THINK everytime)

So, I would rule that you would NOT get to trigger the hounds off of a character put into play via the spheres.

 Well, I am going to send it to Damon.

Magnus Arcanis said:

No need to mail Damon, it's in the rulebook since Day 1.

From the rulebook, p. 14:

Control and Ownership
Players “own” all cards that they brought to the game in their deck.
At the end of the game, all cards are returned to their owners.
When a card comes into play, it does so under the control of its
owner, unless otherwise specified by the effect bringing the card
into play. Some effects also allow a player to take control of an opponent’s
cards.
When an effect refers to “your” card(s) or an “opponent’s” cards,
it is always making reference to the current controller of the card,
unless a reference to the owner of the card is specifically made.
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.

 D'oh!  The Rulebook, huh?  Who'd-a thought to look there!?  

 Yeah and today I got the answer from Damon. Of course, he confirmed what's written in the Rule Book.

mischraum.de said:

So just to clarify, for example, Ulrich plays Revelation of the Spheres and gets a character owned by Dan into play, however, since it enters play under Ulrich's control, it's not considered "an opponent's character" and he is not able to trigger Stalking Hound. Is that right?

AGoT DC Meta said:

It enters under Ulrich's control. So it is Ulrich's character not Dan's. Stalking Hound can't be triggered by Ulrich. Of course if Dan has a Stalking Hound…