(3.26) Duration of Control Change

Unless otherwise stated (for example, with a specified duration), the change of control is permanent until the card that switched sides leaves play or control of the card switches again via a card effect.

Note that attachments that grant control effects end when the attachment granting control leaves play.

So in what situations does the second part of this rule apply? I assume that, in the case of Horn of Dragons, discarding the attachment will not change the fact that my opponent controls my dragon until the end of the phase, correct?

It would come into action with an attachment that states "You control attached character." as a constant effect. I can't find any in the LCG, but Seduced by the Rose (A House of Thorns) seems to fit. In Horn of Dragons' case, it's the ability that gives you control of the character, not the attachment itself.

Right, that's what I figured, I just couldn't find any examples that had any kind of constant control effect, so I thought I'd ask. I was also a little bit hopeful, as a player in my meta recently acquired this card and it's a bit of a thorn in my side, lol.