When opening a savings account for a minor less than 13 years old online a "pop up" box is displayed to capture the consent of the parent or legal guardian. However,this acknowledgement is not retained. Instead the acknowledgement that the "Terms & Conditions" were read is retained. The "Terms & Conditions" includes a parental consent disclosure which ensures the parent receives full disclosure regarding the account and limitations.

Is retaining just the "Terms & Conditions" acknowledgement enough to comply with the “Methods for verifiable parental consent” requirement of the Children's Online Privacy Protection Rule (16 CFR 312.5(b)?

UTMA or joint?

Offering on-line accounts to children less than 13 years old? I hope State law supports that. How do they sign the depositor's agreement?

Joint account

Can you point to a state law that does not allow kids savings accounts if the account is joint with a parent or guardian?

A financial institution/depositor relationship is established through the signing of a legal contract. So "Can you point to a state law that does not allow kids savings accounts", well the answer to that is no. The real question is can you point to a State law that allows a minor in your State to enter into a legally binding contract for a deposit account. Any discussion of whether the account is solely with the minor or a joint account with another person is moot, if your State law does not give them that privilege.

For example, in Texas:

Sec. 34.305. DEPOSIT ACCOUNT OF MINOR. (a) Except as otherwise provided by this section, a bank lawfully doing business in this state may enter into a deposit account with a minor as the sole and absolute owner of the account and may pay checks and withdrawals and otherwise act with respect to the account on the order of the minor. A payment or delivery of rights to a minor who holds a deposit account evidenced by an acquittance signed by the minor discharges the bank to the extent of the payment made or rights delivered.

(b) The disabilities of minority of a minor who is the sole and absolute owner of the deposit account are removed for the limited purpose of enabling:

(1) the minor to enter into a depository contract with the bank; and

(2) the bank to enforce the contract against the minor, including collection of an overdraft or account fee and submission of account history to an account reporting agency or credit reporting bureau.

(c) A parent or legal guardian of a minor may deny the minor's authority to control, transfer, draft on, or make a withdrawal from the minor's deposit account by notifying the bank in writing. On receipt of the notice by the bank, the minor may not control, transfer, draft on, or make a withdrawal from the account during minority except with the joinder of a parent or legal guardian of the minor.

(d) If a minor with a deposit account dies, the acquittance of the minor's parent or legal guardian discharges the liability of the bank to the extent of the acquittance, except that the aggregate discharges under this subsection may not exceed $3,000.

(e) Subsection (a) does not authorize a loan to the minor by the bank, whether on pledge of the minor's savings account or otherwise, or bind the minor to repay a loan made except as provided by Subsection (b) or other law or unless the depository institution has obtained the express consent and joinder of a parent or legal guardian of the minor. This subsection does not apply to an inadvertent extension of credit because of an overdraft from insufficient funds, a returned check or deposit, or another shortage in a depository account resulting from normal banking operations.