Whilst it was true that there was a rumour that BA were considering selling their stake in Qantas after 9/11 I doubt this was true, particularly now that BA seemed to have turned the corner and are starting to make money again.
There is far more to be gained in the long term in keeping the share in Qantas rather than a short term profit in selling it.
Cathay and Qantas are two of the big three players in Asia/Australasia and both members of One World, and although at one time the Star Alliance was seen as bigger and better I think the opposite is now true with the One World alliance consisting of much stronger airlines. Its intention now I think is not to admit any other airlines unless they meet very strict criteria and to concentrate on increasing the strength of the brand with the existing airlines in the alliance.
To that end with Qantas being a very strong and profitable airline in the current world climate, its position in the One World alliance is very important and I cant see any possibility of BA selling its stake in the airline.
On the other hand a day in aviation is a very long time.