Woods has not played since winning the US Open at Torrey Pines last June.
By Russell Fuller in Arizona
In some ways, Tiger Woods was just like any other dad returning from paternity leave: spending his first week away from the family, and looking forward to catching up on some sleep.
Charlie Axel was born two-and-a-half weeks ago - just as Tiger had decided that he was ready to give the rest of the tour some sleepless nights by returning to competitive golf.
The world number one's left knee has been totally rebuilt since he won the US Open last June with a torn anterior cruciate ligament, cartilage damage and numerous stress fractures of the leg.
Ominously, he now reckons that it's in better shape than it has been for over 10 years.
We at the BBC weren't the only ones to jump to Tiger's tune: correspondents from the Toronto Star, The Australian and L'Equipe hastily made travel plans at the end of last week, and many American networks dug out an extra sat track to beam Tuesday's press conference live into thousands of homes.
Once it got under way - 45 minutes late because Tiger had forgotten how long it takes to walk round a golf course - the subject and his interrogators slipped back quickly into the old routine.
"What have you missed the most, Tiger?" asked one hack.
"Hanging out in the press room with you guys," was the gist of the reply - tongue firmly in cheek.
Australia's Brendan Jones - an eight time winner on the Japanese tour - will provide the world number one with his first test of competitive action.
Jones remembers quite literally bumping into Tiger on the way to the locker rooms in Thailand once. Tiger, apparently, doesn't remember bumping into Brendan Jones.
And with that, the American headed out into the Sonoran desert to complete his preparations.
Woods may not be able to reverse the slump in the Dow Jones Index - it's fallen by nearly half since he last played - but he may persuade cash strapped sponsors to sign up again, and he will definitely send viewing figures back in the right direction.
And even though he's won over half of the World Championship events he's contested, that's why his fellow players are so pleased to see him back.
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