Is tench run effected by turbo laser battery ?

Sure. Why wouldn't it?

Trench Run cannot be targeted. Turbolaser Battery does not target anything. So it would work just fine on Trench Run. Any damage already on the Death Star dial would stay there and still count if a second copy of Trench Run was played.

Trench Run cannot be targeted. Turbolaser Battery does not target anything. So it would work just fine on Trench Run. Any damage already on the Death Star dial would stay there and still count if a second copy of Trench Run was played.

Has that second part been officially clarified anywhere, or is it just because the effect speaks of the damage on the dial and not the effect?

Trench Run cannot be targeted. Turbolaser Battery does not target anything. So it would work just fine on Trench Run. Any damage already on the Death Star dial would stay there and still count if a second copy of Trench Run was played.

Has that second part been officially clarified anywhere, or is it just because the effect speaks of the damage on the dial and not the effect?

It's because the Enhancement allows you to place damage on the Death Star dial itself. There's no need for the enhancement to be on the table to keep that damage there (for example, a future event card could read "Place 1 damage on the Death Star dial" and it would work even if Trench Run was not on table, though it would be much less useful without it). The win condition on Trench Run itself only checks for how much total damage is on the dial, not how much was dealt via that copy of Trench Run. Basically, I know that it's a common shortcut (especially on OCTGN) to just place the damage counters on Trench Run itself, but the damage is actually going on the Death Star dial and so it stays there. Somebody could, of course, send in an official rules question if they wanted, but I'm 99.9% sure on this one.

I agree, and like I said, the verbiage seems pretty clear that it goes on the dial and not the enhancement. I was really more curious if it was explicitly clarified somewhere.

Thanks!