I have looked at a lot of sources, but cannot find the proper way to do shingles on one type of eave I have on my house that is not very common. That is the high eave of what I think is known as a shed roof. That is, a roof consisting of one slanted plane without a peak. The roof is asphalt shingles with a 4/12 pitch.
I plan on having an aluminum drip edge product installed on the lower eave (with felt over it) and also on the side rakes (over the felt). I cannot find the conventions for how to treat the high eave. In the past, I was much younger and did it myself, often not knowing how. For example, I stopped the shingles even with the end of the roof decking and applied the same drip edge over the shingle, face nailed and tarred the nail heads. It would seem that there is perhaps a better, larger piece of flashing than common drip edge or perhaps an entirely better way to do this.
Shingle all the way up then add what I call a peak cap, I think you can also use the comp trim just like it was a gable.
There should be a drip edge on the gable, I am too lazy to draw it.
As for fastening it I would screw the vertical section into the fascia. If I was in a high wind area I would screw down through the peak cap (in addition to the other fastener) and shingles into the deck. I would not use a nail and tar...a screw with a gasket would be better. And yes, it is larger than the normal drip edge on top...I like 4 to 5 inches.
Depending on the roof product and where my courses fall will determine the actual dimensions of the peak cap. It is usually custom made to the actual pitch of the roof so it is not a stock item.
If you didn't want to see any fasteners you could do a two piece system. The first piece is nailed down and we call it a cleat and the peak cap would snap into it...far more complicated than needed but a cleaner look.