@Curious: I think every kid/parent/family dynamic is different in this regard. I probably did more than some parents in terms of helping her shape the initial list and requesting info/setting up appointments, etc. But as I think I noted on my “One Family’s” thread, my kids don’t set up their own doctor visits; nor do they do that much legwork when it comes to planning family vacations (something else that can require a bit of online research). Happy to report that 7D1 is happily and actively advocating for herself in her first year at college. Keep in mind that many BS applicants are only in 8th grade and my older girl was a year younger than most of her classmates at that point already.
I do think that while a parent can plant the seed of “going to boarding school” and help shepherd his/her kid through the process, the kid has to really want it to happen for it all to work. And of course, the kid has to write his/her own essays (though I believe parental proofreading is fine).
My younger daughter is a fencer, but after years in the sport, she still doesn’t select and register for tournaments on her own. After all, I am the one paying and driving (and flying sometimes) to these things, so I like to have a little more say in which ones we go to! 
I have heard of other families where the kid “drove” the process more in terms of doing initial research, etc. Again, I think every family will have a different dynamic and a different vision of what feels right.