...the decision to go paperless...could apply to all the accounts they own, or just the ones they select.
Obviously, this is a customer service issue, but it's also an ESIGN issue. Part of the consent process is to establish which documents will become tree-free. The bank's standard consent process can have blanket coverage or you can go ala-carte, but you
must have the informed consent of an authorized party for the switch to be valid, document by document.