How wide is the door?
Even if you do it as Lester's detail shows, if they use two pieces of j channel because the door is wider than the j they have ( and everywhere else j is used as a bottom catch ) then there is a break letting the water through when the j has water in it when it rains where the peices **** together.
I don't know if anyone has a good fix for this issue... and where the j ends and is supposed to spill the water off the sides ( but somehow not under the siding).
The door surround piece is one piece at the top, and one piece for each side (no seams).
The J trim goes outside, over the top of the surround trim, and the J trim is one piece and is open on each end.
No fix needed.. it works.
Folks tend to use J-trim in areas it was never intended to be used. On my barn the only place it is used, IIRC, is above the overhead doors, and the man door. None are spliced.