Not only through puberty but some until only several years ago. Perhaps puberty for me lasted into my 50s! I would say I was discharging through my face the crap I put into my system when I was young.
No, not on my entire face. I did, however, get one big whopper of an insanely gross-pussing, all-encompassing, GIGANTICALLY HUGE ZIT on my left nostril. Right where your nose joins your face. This popped up about once every other year.
Man, those were Mt. St. Helens' size mongers. They hurt like a big dog, too.
Not during puberty; but a couple of pimples have sprouted recently: one on my back, and one at the back of my neck. I wonder if that is a sign of imminent onset of menopause. There are other indications as well.