Bankers have come to view America Online, Prodigy, and Compuserve - the three traditional on-line service networks - as additional options for being wherever and whenever customers want to do banking. They are part of a delivery-system continuum that begins, and circles back to, the branch.

In September, Sanwa Bank of California filled its branches with free America Online T-shirts and computer disks. The hoopla coincided with the launch of BankNow, the home banking service created for AOL by Intuit Inc.

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