Perhaps this is a stupid question, but I am curious about how borders work when they run "through" lakes. For example, the Great Lakes. On one shore, you're in Canada. On the opposite shore, you are in the US. My question is, do the borders of those two countries run through the middle of the lakes? Or do they hug the shores of the respective countries? And if the answer is the latter, then to which country does the middle of the lake belong?

The borders run through the lakes, not along the shores.

US-Canada borders through Great Lakes (https://maps.google.com/maps?q=great+lakes+border+us+canada&oe=utf-8&client=firefox&ie=UTF-8&ei=3-khUoivCoqU2gWQ_4D4Bg&ved=0CAoQ_AUoAg)