Brief overview: Yahoo! has been using Google's search results to power its organic search service. Yahoo!, over the past year, has purchased several search engine technologies - including Inktomi and Overture (which at that time owned AltaVista and AllTheWeb).
The main speculation was that Yahoo!, since it purchased Inktomi right out, would be using Inktomi results after it leaves Google. We have also seen cases where Inktomi results have been experimented with Yahoo in the main stream search and largely overseas.
Grumpus a moderator over at cre8asiteforums posted at HighRankings Forum his opinion that Yahoo will not being using Inktomi but rather AllTheWeb and/or AltaVista.
Very interested information, read more about it at http://www.highrankings.com/forum/index.php?showtopic=2826.