Last month, I told you that Google (NASDAQ:GOOG) CEO Eric Schmidt should resign from the board of Apple (NASDAQ:AAPL). With potential conflicts of interest arising between the two companies in fields as diverse as cell phones, operating systems, and Web browsers, it was time to sever the tight-knit ties between Cupertino and Mountain View.

That argument finally struck a nerve at Apple: Schmidt has stepped down from his duties at the company. "Eric's effectiveness as an Apple Board member will be significantly diminished," said iconic Apple CEO Steve Jobs, "since he will have to recuse himself from even larger portions of our meetings due to potential conflicts of interest."

Right on, brother.

Apple hasn't named a replacement for Schmidt yet. When that announcement comes, you should expect to recognize the name. The board is packed full of luminaries like J. Crew CEO Willard Drexler, former Intuit (NASDAQ:INTU) CEO Bill Campbell, and almost-President Al Gore.

By no means have all connections between Apple and Google been destroyed with Dr. Schmidt's resignation. Mr. Gore still holds an advisory position with Google while serving on Apple's board, and former Genentech CEO Arthur Levinson sits on both boards. I don't think it'll happen, either -- nobody important has called for their resignations from either company.

Cross-pollination between the giants of industry is perfectly normal and probably good for business in general. For example, former Yahoo! (NASDAQ:YHOO) COO and heir-apparent Susan Decker holds a very interesting set of top-level board seats at chip designer Intel (NASDAQ:INTC), Warren Buffett's Berkshire Hathaway (NYSE:BRK-B), and Costco Wholesale (NASDAQ:COST). It's just that the competition between those cross-boarded businesses tends to be less direct than what Google and Apple are shaping up to face.

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