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Here is a link [inktomi.com] to the Inktomi page where they list their most important search partners. I've never seen a list of all the 100+ partners.
Yes, if you get a page in the Inktomi database, all the Inktomi search partners will have access to your page. Each partner can customize their own version of the Inktomi database, and even add in other data of their own -- so you can never be sure where your page will show up on any particular Inktomi partner, or how highly ranked it will be.
I'd suggest reading through the info on this Inktomi forum to get a good feel for how things are right now, how Inktomi combines the paid and unpaid submissions, etc. It's definitely not necessary to submit to each individual partner, and might even hurt you -- for instance, a while back, pages submitted through Anzwers were penalized as spam if they weren't Australia-New Zealand sites.
Don't miss this conversation [webmasterworld.com] about getting pages into Inktomi without submitting. If you are not doing paid submissions, it's certainly a method you should think about.