I actually have related question.
I'm trying to find solid information on Google's criteria on showing a "mini Google search box" within sitelinks?
Example: if you type-in "wikipedia" on Google.com, a mini search box appears within the site links. This is for organic listing not paid listing.
The Google Support page on Sitelinks does not state any info on the mini google search box. http://support.google.com/webmasters/bin/answer.py?hl=en&answer=47334
Any help?