It all depends on where you are, and what school you attend. I am completing a PhD in Canada at one of Canada's Tier 1 universities. I own the copyright to all my work, my notes, my essays, my papers (except those that have been published by a major journal), my blog posts, and my dissertation. And yes, I am funded by the university and a provincial agency.

To get my degree, I grant the university (and the National Library) a non-exclusive license to reproduce my thesis in their respective databases, but I hold the copyright. It even says so on the cover page. In fact, at my university, we even have the option to license it under Creative Commons (which I intend to do when/if I'm done).

The reason this doesn't apply to Canadians has to do with cross-border transport of both finished goods and raw materials. Truckers from both Canada and the U.S. routinely cross the border to minimize transportation distance (among other things, like providing just-in-time inventory supply). Doing the whole fingerprint/photograph thing would interfere significantly with commerce and manufacturing in both countries, so that's why the exception.