Sharp corners corners will burn away like RobX4406 said, and like P body said, put the heat into the thick piece, and persuade it to the thinner piece.......
Just make sure you practice on some scrap, before you get going to heavy.......
.....and as far as the tie ins, if you grind/blend in the starts/stops, the weld would theoretically be as strong all around.
Had to get re-certified for a particular contractor's job a couple months ago(316 stainless, 6" sch. 40, TIG root/hot pass, Flux core cap)100% x-ray, and had two starts in it on the cap(slipped
)
Trust me, it does not make a difference whatsoever if you are thorough in the prep/tie in/heat control.......