Posing a question about a very interesting point that was made by Marcia in another thread.
We have suffered a PR downgrade recently and the reasons why are being investigated. There has been no impact on our US site.

Background
We have two sites, very different in design.
Both sites (US and European) are totally managed (registered, designed, hosted, maintained) in the US.

Could Google think that the European site is intended for a US audience.?
Whereas the site is intended to support the EMEA area.

Where Google has specific country search engines (eg, .co.uk for UK), how does it know local .com websites. Or does it.?

There's never been any evidence that a loss of PR would be geographically influenced in any way, that's a different issue from ranking.

Where Google has specific country search engines (eg, .co.uk for UK), how does it know local .com websites. Or does it.?
They do, and it does make a difference. The difference can be detected by the geographical location of IP numbers.

To rank country-specific, it takes having a local TLD and/or being hosted (preferably both, most likely) within the country itself, which would be evidenced by detecting an IP number local to that particular country.

There are several different local filterings in place - some is language specific and some is location specific. Some countries default to location and some to language.

Language targeting is easy but location targeting is tricky. The best thing is to have a local server with a local IP but getting lots of local links - especially from veryfied local sources like Yahoo and regional ODP categories, seems to help.

However, none of this will impact your PageRank. Thats a different game

To assist our ranking (at least not hinder), would you suggest that we host our European site in Europe.?
The site is not country specific as it is intended to support EMEA.

you may want to host it in your target market where you feel the most demand will be?