Bank of Internet USA is relatively small, but its rapid growth has led its top executives to make some ambitious - some might even say grandiose - predictions.

Last month it reported that its assets jumped 16% in the second half of last year, to $316.8 million at yearend. And Jerry Englert, the chairman of the San Diego Internet-only savings bank, said in the earnings report, "We believe Internet self-service banking will likely be the dominant consumer choice in the near future."

In an interview Feb. 10, he said he expects more people to flock to his institution and others like it and drive those figures even higher. "The idea here is that money is a commodity, and those who can deliver that commodity the least expensively will ultimately win the battle."

Internet-only banks like to say that because they do not have to maintain branches, they can offer better interest rates and lower fees than traditional banks. But despite these perceived advantages, some of Mr. Englert's Internet competitors are less optimistic.

Frank Trotter, the president and chief executive of another branchless savings bank - the EverBank National Banking Group division of EverBank Financial Corp. in Jacksonville, Fla. - said Mr. Englert's prediction in his earnings report may not have been off-target, but it was rather bold.

"We will see tremendous growth, but 'dominance' is putting it a bit too hard," Mr. Trotter said.

And David Lewis, the chief marketing and IT officer at ING Direct, America's largest Internet bank, agreed that Mr. Englert's prediction of dominance was premature. "In the near future? Probably not. But eventually? I would say yes."

No matter how popular direct banking becomes, the ING Group NV unit does not expect the format to completely replace retail banks. Arkadi Kuhlmann, its president and chief executive, says his institution is not competing with standard banks in day-to-day banking activities. "We see ourselves not as a primary transaction account, but as a reserve. We really are your savings account."

But Mr. Englert says he is watching online banking become dominant, almost before his eyes. When asked exactly how soon it would become dominant, he replied, "It's occurring as we talk."

And talking helps encourage this growth, he said. Mr. Englert credits word-of-mouth for expanding ING Direct's customer base. Wherever a new customer signs up, several more do so nearby within days, Mr. Englert said.

"You can just watch pockets of customers appear," he said. Mr. Englert compared branchless banking to the airline industry, where more than half of all tickets are now purchased online.

However, Penny Gillespie, a senior analyst at Forrester Research Inc., said the comparison works best if those airline passengers travel without luggage. Until we become a paperless society, the physical aspects of consumer-level banking - including personal checks, deposit slips, and of course, cash - will survive, she said.

"Currency is a physical thing," Ms. Gillespie said. "Deposits and withdrawals, depending on the nature of those transactions, are still physical."

But debit cards are helping pave the way to a paperless system by allowing consumers to make instant payments from their checking accounts and even allowing them to request withdrawals from cashiers at the grocery store or post office without being charged an automated teller machine fee. (In fact, the Web sites for several Internet banks suggest that consumers do just that.)

"No one actually wants to get in their car and drive to their local bank," Mr. Lewis said. "They have to, because they have this paper check."

Many other countries have moved more rapidly to adopt electronic payments in lieu of checks, but U.S. businesses and government agencies are expected to start making more payments in digital form, he said. For consumers, however, checks remain the most common method of making payments to individuals. However, "direct banking will dominate as paper checks fall off in their importance."

Though Ms. Gillespie says that "certainly internet banking is growing," she takes issue with Mr. Englert's predictions about the growth of direct banking among consumers. "That's a very bold statement, considering that 80% of all [checking] transactions are still done at the branches."

Ms. Gillespie's research indicates that just 13% of U.S. checking transactions are performed through a Web site, versus the 12% performed over the phone.

In 2002, Forrester estimated that 20% of U.S. households with an Internet connection were using it to perform bank transactions. That number was forecast to rise to 22% by the end of last year, 24% by the end of this year, and 35% in 2008.

The numbers are a bit thinner when including households without Internet connections, but Forrester still predicts strong growth for Internet banking - from 13% of total households in 2002 to 26% of total households in 2008.

Chris Musto, a vice president for research at Gomez Inc. of Waltham, Mass., said one in four American adults that have checking accounts and use the Internet are also using online banking.

But these figures don't measure the popularity of online-only banks or whether customers also visit branches. And clearly, direct banks are not replacing traditional bricks-and-mortar ones. "No one's going out of business because of" Internet banking, Mr. Musto said.

Check writers and debit card users alike are still tethered to their branches, but Mr. Musto said there is one example where branches have been essentially abandoned - branchless cards.

Over time the Internet has become more important to credit card issuers, who no longer need to maintain a physical office near their customers, he said. "The branchless credit card approach had been going on for years and years before the Internet was even invented."