Just to confuse the matter even more, the newer Trent's are certified as RB211 derivatives. A Trent 700 on the A330 is certified as a RB211 Trent 772 etc. (
http://www.easa.eu.int/ws_prod/c/doc...700_series.pdf).
The Trent series of engines (T500, 700, 800 & 900) are all built on the foundations of the original RB211-22 with the fan and core scaled appropriately and the incorporation of new technologies over time.
The Trent 1000 (B787) is the first of the Trent series to be certified purely as a Trent 100 and not as a RB211 derivative. The EASA Type Cert can be found here...
http://www.easa.eu.int/ws_prod/c/doc...00%20FINAL.pdf
All the best,
P2C