Trent 1000 my friend. Trent 1000. (airbus 380)
I just got back from visiting the Rolls-Royce & GE sites... curiousity was getting to me and I just couldn't take it anymore.
Shame on you for getting that one wrong! (On more than one account.)
The Trent 1000 is the new engine for the 787 - a plane that's smaller than the 777 - about 767 size. Doesn't seem reasonable that engine would need to be bigger than the 777's. The Trent 1000's fan is only 112", with thrust ratings in the 53,000-70,000 pound range.
The Airbus (yuk, the "A" word) A380 uses the Trent 900. Fan is bigger than the 1000's, but is still only only 116" and rated in the 70K-80K range.
The GE90-115B (used only on 777-300ER & 777-200LR models) is still bigger and more powerful than either one of them - at least according to The Guiness Book of World Records.
If either one has a bigger fan, or more power, they sure aren't claiming it. The -115B has a 135" fan and has managed 127,900 pounds of thrust (sustained).
Even the smaller GE90-94B (used on other 777 variants) is bigger and more powerful than the Trent 900 or 1000. It has a power rating similar to the Trent 800 (also used on 777's that aren't -300ER or -200LR variants), but still has a bigger fan (only 1" smaller than the -115B's).
Not to insinuate in any way that the RR engines are worse than their competition in quality, just the (published) fact that the GE90-115B is the biggest and most powerful jet engine in production today.