Custodian Act

whose SSN is on a/c. if it's your's you need to report it in and out (as nominee)

returns have to be filed for the kids if any of the following apply (they apply to each child)

• their unearned income was over $1,100. 
• their earned income was over $12,200.
• their gross income was more than the larger of—
• $1,100, or
• their earned income (up to $11,850) plus $350

by the way, I hope you have separate custodial a/cs for each child.  there are legal issues that could arise that makes having a separate a/c for each child important - but this varies because the laws regarding these a/c's vary from state to state. 

if you may a gift of more than 415,000 to either child, you should be filing a gift tax return

here's some info about such a/c's

The UGMA/UTMA setup is commonly used to give monies to a minor. IRS regulations allows a person to give many thousands of dollars per year to any other person with no tax consequences. If the recipient is a minor, the UGMA provides a way for the minor to own the assets without involving an attorney to establish a special trust. When giving assets to a minor using a UGMA/UTMA, the donor must appoint a custodian (the trustee).

You use the minor’s social security number as the taxpayer ID for this account. When you fill out the W-9 form for this account, it will show this form. The custodian (which is the person who gave the child the money)  should certify the W-9 form.

The money now belongs to the minor and the custodian has a legal fiduciary responsibility to handle the money in a prudent manner for the benefit of the minor.

Handling the money “in a prudent manner” means that the custodian can buy common stocks but cannot write naked options. The custodian cannot “invest” the money on the horses, planning to donate the winnings to the minor. And when the minor reaches the age at which the UGMA becomes property of the minor (who is either 18 or 21 depending on the state and not a minor any longer), the minor can claim all of the funds even if that’s against the custodian’s wishes. Neither the donor nor the custodian can place any conditions on those funds once the minor becomes an adult.

so if your planning to have the funds used for college but the child, now an adult, wants to use the money to buy an airplane, you have no say.  many donors have come to regret these types of a/c's because they lose control eventually.   there have even been lawsuits when a donor spends the money on the child's behalf after the child becomes an adult.