You can leave them to ripen on the stem and let them self seed if you want that. They pop up in interesting places you would't think to put them. Or save ripe seeds and plant them whatever way you want. Globe alliums look best casually planted.

Just remember that it will be about 3-5 years before the seedlings bloom.

It's best to dry the whole stem for the winter, they look lovely indoors !

One end of my island border is allowed to run itself, with a touch on the tiller, every so often. Most alliums seed themselves well. Some can be a nuisance too. The globe allium is very good at that. Some of them bend over the stem with the globe on the ground. If you want to leave it there, it will ripen its seeds and sew itself. The bulbs do not burrow down far so you can get at them if you want to have your way. They take a while to bloom but you don't really notice if you don't tinker around them too much.