One of the tricks you can do with the Active Directory Federation Services (ADFS) home realm discovery process is get a user to skip the home realm discovery page completely if you embed a query string in the application URL that tells ADFS what realm to use.  The query string is:

whr=xxxxxx

where xxxxxx is the federation URI of the partner (which they tell you when you set up your federation, or you create when you are setting up your test lab).  That typically looks like:

urn:federation:myorganization

Thus, the whole url might look like:

http://www.joekaplan.net/?whr=urn:federation.myorganization

(no, this site is not federation-enabled and won't be any time soon...)

Using these home realm query strings is very handy, not only for getting your own organization's users to the target app quicker by allowing them to skip a page that may potentially have many choices, but also just for testing.  The query string overrides the persistent cookie you may have that identifies your home realm, so you can use this to avoid having to delete your cookies all the time.

However, if you want to refer to the resource partner's account store with this trick, you don't use the resource partner's federation URI.  Instead, you use the "built-in" URI:

urn:federation:self

I'm sure this is probably documented somewhere (or maybe not; the ADFS docs have a ways to go...), but I had to figure it out the hard way and I thought I'd share.