I think the first 16 777s BA ordered were with GE90s - thereafter it was Rolls all the way! That should be 29 777s with Rolls engines by my reckoning, assuming it was just the first 16 with GE90s - 58 engines in total.
The ultra long reach 777 jobbies (the one that came out a month or two ago, and the other one next year - competing with A340-500 & -600) are powered solely by GE90s with max thrust rated at 115,000lbs each! General Electric managed to secure the contract with Boing to be exclusive engine supplier for these two variants; I believe at quite a high cost for GE.
Boeing got a bargain but it reamains to be seen whether having only GE engines being offered will affect new orders for the long range variants.
