As part of the PlayStation Network's guidelines, minors must create a Sub Account under a parent or guardian's Master Account, and are subject to spending limits imposed by the Master Account's payment options. Until recently, however, Sub Accounts were unable to upgrade to Master Accounts even after a user turned 18; Sony instead recommended that "the sub account holder should create a new master account when they reach 18."
Account transition functionality is now available upon request for PlayStation 3 users, and will be accessible for PlayStation 4 owners when the console launches later this week.
[Update: Contacting Polygon, a Sony representative explained that account-upgrading functionality is not yet in effect. "Sub accounts can't be upgraded to master accounts on any PlayStation platform," the representative said. Asked for clarification, the representative added: "We don't have any additional comment at this time."]
Sony PlayStation 3 (late 2012)
Sony PlayStation 4