>>a polity ruling over huge territories and many people, in which rule is not based on explicit consent by the governed; it is a very great power that defines the international system and is linked to a great culture.

>I think Canada and the US (and possibly Mexico) are empires by that defintion, but perhaps not in the way you meant. The US and Canada started as small countries on the east coast of North American then expanded via the use of military force, military strength and coercion.

"Consent of the governed" is the key phrase - in fact, I think it is the distinguishing characteristic between countries and empires. The formal states that compose the US are included because of this. Once you include Puerto Rico - well, things become a little greyer. For Canada, you have the whole Quebec issue. Mexico is big, but not liable to split up any time soon; I would put it solidly in the "country" category. Same for Brazil. Big place but a pretty homogenous population.