A. The rules on transferring ownership of your child's custodial account to him vary by state and account.
There are two key ages:
a) the age of majority (often 18)
b) the age of termination on the account (usually 21)
When children reach the age of majority, the account can be transferred into their names only with custodian consent. Otherwise, they can remove the custodian from the account at the age of termination.
You can ask your brokerage firm what ages apply to your child's accounts and the steps you need to take at each point.