Hi
Lyman,
With what information has been provided on the Trent 1000 engine gearbox, it is not possible to know which component had the corrosion problem as the gearbox is jam packed with components of different materials.
Relative to comparison to the Trent 900 engine, the Trent 1000 gearbox would be significantly different as it would be customized for the Boeing 787 application. For the Trent 900, the gearbox and radial drive would look something like this except the radial drive shaft would be angled forward and the gearbox itself is mounted on the fan casing. The power is taken from the HP compressor shaft as it is a three shafted engine design.
For the Boeing 787, the gearbox is mounted just behind the fan casing. It is different as this aircraft is an MEA (More Electric Aircraft) than the Airbus A-380. For one thing, there is no longer hot bleed air taken off the engine compressor which was used for cabin pressurization, nacelle & wing ice protection and engine starting. Bleed air is replaced by electric generators to perform these functions and others. This means the mechanics inside the gearbox are changed to accept these larger generators that were not required in a more conventional aircraft. The design, function and ultimate location of the gear box is a team effort by the aircraft designers, engine manufacturer and gearbox producer. The engine folks used to do the design and even the gearbox assembly at one time, but that has changed as there are companies that specialize in this complicated item today. RR chose Hamilton-Sunstrand a division of United Aircraft Corp. (think Pratt & Whitney), while GE chose Avio Group in Italy for their gearbox on the GEnx1-B engine for the B787. You can see what the GEnx1-B gearbox looks like by going to this site:
http://www.aviogroup.com/files/catal.../genx_eng9.pdf
As the article points out, the gearbox for the GEnx2-B is different from the 1-B engine as the Boeing 747-8 is more conventional and still uses engine compressor bleed air. In a conventional aircraft during engine starting, the gearbox runs in reverse to help start the engine in case you didn't know.
Hopefully, this answers at least part of your question/comments...