Everyone with a child. Or half of them anyway, since it goes to one parent only (at least for parents that live together).
It's not really transferred to the child at age 16. What typically happens at that age is that the child has completed all mandatory years in school and move on to optional education and then they get paid for studying.
Yes, sorry I mis-explained the 16-year thing. I think one highlight of that is that the benefit shifts to being paid by the CSN (Sweden board of student finance, they are the ones who provide subsidized student loans as well) and it is tied to you being a student. So if you drop out of high school you stop getting this benefit.
It's not really transferred to the child at age 16. What typically happens at that age is that the child has completed all mandatory years in school and move on to optional education and then they get paid for studying.