How Steve Jobs spent his last days

The book, in stores Tuesday, is based on in-depth interviews by authors Brent Schlender and Rick Tetzeli with leaders in the technology and entertainment business and Apple (AAPL, Tech30) executives who worked closely with Jobs.

In one notable passage, current CEO Tim Cook remembers the day when Jobs asked him to take the top spot.

At that time, Jobs was battling cancer and was spending much of his time at home. He called over Cook, who was then Apple's chief operating officer.

Cook recalls that he and Jobs discussed what it would be like for Cook to be CEO while the notoriously controlling Jobs would become chairman of the board.

''I tried to pick something that would incite him. So I said, 'You mean that if I review an ad and I like it, it should just run without your okay?' And he laughed, and said, 'Well, I hope you'd at least ask me!' "

Jobs was so closely identified with Apple that it was hard to imagine the company under any other CEO. But Cook says that Jobs wanted a successor who wouldn't try to replicate what he had done. Jobs referred to it as the "Beatles concept," where each member of the iconic band had talents that complemented each other.

Related: 6 things about 'Becoming Steve Jobs'

Jobs' health took a turn for the worse just eight weeks after this conversation. Cook says in the book that he watched a movie with Jobs the Friday before he passed away.

"We watched Remember the Titans [a sentimental football story about an underdog]. I was so surprised he wanted to watch that movie. I was like, Are you sure? Steve was not interested in sports at all. And we watched and we talked about a number of things and I left thinking that he was pretty happy."

Related: 5 things Steve Jobs said Apple would never do - and Apple is doing

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How Steve Jobs spent his last days