Scenario: I first logged in to the SE site "A Curious Home" and associated my Google ID via the stackexchange.com-based URL of http://acurioushome.stackexchange.com.
However, when I try to login with my Google account via http://www.acurioushome.com, which I expect is to be the real/final URL, the site doesn't actually recognize me as the user I created originally via the SE-based URL. Instead, it shows "unknown (google)" at the top of the page.
Considering that, should StackExchange site URLs be published with both types of URLs as this site has (probably not?), or just one, or the other?
It seems the way Google's Open ID implementation works that it's best to launch and keep just one URL.