Multi regional domain strategy same branded sites

How to get the best overall results and keep Google happy

[Whitey]

Does Google mind multi regional sites of the same brand / same owner appearing in it's results?

We want all three of the same branded large sites [ 80k pages each ] to return to producing full results, following an overhaul of dupe content, URL fixing and site architecture alterations, [ done last August ]. To date one site is producing well - and it only burst back onto the scene 8 days ago. The other two only produce a flicker of results on Google at this point, except on obscure terms.

On these obscure results [ where no one really competes for positioning ] we sometimes find that we have three out of the top 10 results. In the future, on common terms, heavily competed for, we would try to avoid this number of results occurring in the top 10 and thus avoid the possibility of being perceived by Google as "spamming" results.

[ I do get cranky when i see competing sites using sub domains with the same keyword to dominate pages - i think it's in nobody's interest in producing quality results ]

The multiple domains have different regional extentions for the purpose of making the results available in local markets via localised search filters.

e.g.

oursite.co.uk - seeking strong UK related rankings & obscure terms
oursite.ca - seeking strong CA related rankings & obscure terms
oursite.com - seeking strong overall global rankings except above

We restrict our localised ranking activity to the most relevant of pages for each of the regional sites, and reserve "heavy duty" SEO/ranking activity for the .com site. We are also cautious to avoid duplicate content scenarios and do not cross link those sites.

But what do you think Google tolerates and supports for site's with multiple regional extentions?

Is there a "best practice" to keep the SE's , visitors and site owners happy?