The fraction of U.S. households doing at least some of their banking online has grown from about 20 percent in 2002 to just under 50 percent today, according to Forrester Research. Over the long run, that trend will probably favor bigger banks, said Ed Nelling, a professor of finance at Drexel University in Philadelphia. “As technology evolves over time, people will get more comfortable with an anonymous working relationship with banking,” he said.