You are dealing with two sets of rules that need to be separated in order to design your e-delivery system.
ESIGN spells out the requirements for getting the customer's permission to substitute electrons for paper. (See Section 101(c) of ESIGN.) It's a disclosure & opt-in system. Disclosures to the customer may be on paper or electronic, but they must explain the hardware & software requirements the customer must meet in order to receive, use, and retain the e-statements. Opt-in must be handled in a manner that "demonstrates" the consumer's success in using the required medium. Demonstrating success involves more than simply getting the customer to agree to e-delivery--somehow there must be feedback to the bank proving that the customer has been able to receive and use a test message of the type to be used "for real."
Having gotten the customer's consent, you now turn your attention to Reg. DD (for deposit statements) or Reg Z (for HELOCS, credit cards, etc.) for the specific rules governing the delivery of required disclosures. In March/April 2001, the Fed issued "interim final rules" addressing e-delivery. These rules outline a system you must follow in order for your electrons to meet the Fed's minimum standard for "written" disclosures under these regs.
You face two serious risks if you don't set this up correctly.
First, by failing to meet ESIGN's requirements, your electrons would not constitute a legal substitution for paper. That means the disclosures you thought you delivered don't count. Add up the civil liability. Update your resume.
Second, failing to implement your delivery in accordance with the interim final rules (or some alternative that accomplishes the same thing and will pass muster during an exam), your disclosures may not count, or may be judged to be flawed. Add up the civil liability. Update your resume.
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...gone fishing.