This is something that will vary by household. Every situation is unique, and every culture has its own approach to growing up. We usually view growing up as a gradual release of responsibility. This means that at some point along the way the parents will relinquish some responsibility to the children. When that happens depends on the parents and the children.
Children need to learn how to make decisions on their own. If they do not learn how to make small decisions, and then larger ones, they will not be successful adults. The rise of “helicopter parenting” in our culture has brought attention to parents who try to protect their children from all possible harm and make all decisions for them, but parents making decisions for their children is nothing new. Again, it depends on the culture and the time period.
Legally, parents have the right to make decisions for their children while they are still minors and under 18. However, responsible parents will teach their children how to make good decisions from a young age. Teenagers often have other influences in their lives that lead them to lose perspective. Parents sometimes need to intervene and make better decisions. The teens may not realize until later that their parents saved them from disaster.