There isn't exactly such a thing as your Inktomi position, because every partner takes their own customized data from Ink and many of them integrate other results into their database as well. I have had pages that are #78 on HotBot and #5 on MSN at the same time. Others show as listed if I search on the URL, but are buried too deep to matter.
Right now I watch MSN, HotBot and Canada.com to get a feeling for my Ink listings. AOL uses Inktomi data as well, but there are too many other things happening there for it to be much of an indicator.
The Ink spider (Slurp) will be the only one crawling your paid Ink listing page(s). It comes by no less frequently than every 48 hrs. (Sometimes I see it as frequent as every day). It sends it's results to Ink's database. Not sure how often the database is updated, though.
It's the database results that get farmed out to Ink's partners....MSN, Iwon, etc.... and they do with it what they do with it.