Hi Tucker;

I have only seen a few buildings with a common purlin roof system with gable overhangs here in northern New England. In the examples I have seen the purlins are trenched into the principals with the tops flush and the gable ends the purlins simply cantilever a foot or so to form the overhang. The projecting part of the purlin is called a lookout: See figure 29, page 8 of this link.

http://www.tfguild.org/joinery/part5.pdf

On the sidewalls the tie beam can cantilever over the top of a post or an English tying joint with what I call an eaves purlin like this:

http://i121.photobucket.com/albums/o223/jimderby/th_IMG_0667resized.jpg

Or frame the overhang separately such as using "sprocket", see figure 8, page 3 in the same link as above:

http://www.tfguild.org/joinery/part5.pdf

In French work this sprocket is called a coyau and can be set at a lower pitch producing a bellcast (bell-cast, belcast) roof.

I have not seen a historical example but, at least in Eastern work, their are rafters called fan rafters which angle out to frame the corners of the roof overhangs. I do not know of a Western example to show you but you can see some fan rafters at this link:

http://thecarpentryway.blogspot.com/2010/10/fan-of-fan-viii.html

Good luck;
Jim

The closer you look the more you see.
"Heavy timber framing is not a lost art" Fred Hodgson, 1909