The search for an answer will frame succession planning discussions in Building 4 of 1 Infinite Loop -- the heart of Apple's California headquarters -- when Cook is expected to step in for his boss to lead the annual shareholders meeting on Wednesday.
But little did Cook know that a gut decision he made in 1998 during his first meeting with Silicon Valley legend Steve Jobs would forever change his life -- and alter the course of technology history.
Today, the heir presumptive at Apple has to prove his technology instincts are as sharp as when he elected to jump ship from the once-mighty Compaq, which was then the world's top PC maker, to an Apple in the 1990s that was barely afloat.
"My most significant discovery so far in my life was the result of one single decision, my decision to join Apple," a reflective Cook told Auburn University students at his alma mater last year. "Working at Apple was never in any plan that I outlined for myself, but was without a doubt the best decision that I ever made."
Indeed. Cook, the perennial No. 2 working behind the scenes throughout most of his career -- he was even second in his high school class -- is finally stepping into the limelight.
With Jobs out on his third medical leave of absence and deemed by many unlikely to return, Cook may finally get his shot to be number one at Apple.
But what most investors want to know is whether Cook possesses any of Jobs' instincts for anticipating what consumers want before they know it.
Those who have known or worked with Cook over the past two decades speak of him in reverential tones, using terms like "brilliant" and "phenomenal." Still, after years of relative anonymity as Jobs' No. 2, Cook remains untested.
He has one thing in his favor: the sheer competitiveness he shares with his boss.
"He's not in it for the fame or the ego or the money. He's in it to win," said Greg Petsch, who was Cook's boss at Compaq Computer back in the late 1990s.
How Cook got his turn is now part of Apple legend. As recounted in the Wall Street Journal, Jobs, then newly returned to Apple to salvage a sinking ship, had turned down several applicants in characteristically brusque fashion, including walking out midway through one interview.
By Cook's own account, they took to each other instantly, and Cook made his fateful decision. He was told he would be a fool to leave Compaq for an also-ran on the verge of bankruptcy. But his mind was made up.
"I listened to my intuition, not the left side of my brain," Cook said.
Despite their quick connection, Jobs and Cook are a study in contrasts.
Where Jobs is famous for his explosive temper -- firing employees on the spot -- Cook is described as down-to-earth and a gentleman, even soft-spoken.
Where Jobs is known for his New Age interest in vegetarianism and spirituality, Cook hails from an Alabama town, loves Auburn U football and is a fitness fanatic.
And where Jobs enjoyed rockstar-like fame early in his career as a pioneer of the computer era, the intensely private Cook toiled for years in obscurity, an operations wonk who became chief lieutenant at one of the world's coolest companies.
Cook has since built a formidable reputation as an operations genius, credited with helping resuscitate Apple after its tailspin in the 1990s and transform it into the powerhouse of today.
"He has a steel trap of a mind," said a person who worked with him at Apple. "He not only knows everything about what he's doing, he knows everything about what you're doing too."
Some say that Cook's achievements, not to mention his skillful management of Apple's resurgent Mac unit, show that he is much more than just a by-the-numbers supply chain expert.
"They call him an operational genius, but Tim's a lot more strategic than he's been getting credit for," said Petsch.
Although operations executives are not generally considered CEO material, Petsch pointed to former Intel CEO Craig Barrett's rise to the top from COO jobs.
And others argue that it is outdated to think of Apple as simply a vehicle for Jobs' savant-like technology vision.
They note that Jobs has for years been surrounded by a superbly talented management team -- executives like design chief Jonathan Ive, mobile software guru Scott Forstall and product marketing head Phil Schiller -- who would be there to complement Cook.
"My sense is that he would not have to be the end-all be-all for product vision," said the person who worked with Cook. "It would be that team of people that Steve has been working with for awhile. They bring ideas to him."
There is little question, however, that much of the Apple mystique revolves around Jobs, their iconic leader.
Jobs' far-sighted, sometimes counterintuitive approach, has guided Apple to a string of triumphs over the past decade. The iPod, iPhone and iPad, ideas which have reshaped both personal computing and entertainment, have made Apple one of the most powerful companies on the planet.
He remains the final authority at Apple, the man who with a word can create a product or shelve it. He is famous for his blistering attention to detail. In one oft repeated anecdote, Jobs demanded the dismantling of the original iPod the night before the press launch, when he noticed the headphone jack did not make a satisfying click when headphones were inserted.
Although Jobs remains involved in strategic decisions and has recently been seen at Apple's headquarters, Cook runs the company day-to-day.
Still, living up to the expectations of investors and Apple's passionate fan base is an enormous challenge.
Cook himself has acknowledged that Apple's headquarters in Cupertino, California, is a long way from his roots in Robertsdale, Alabama, calling his journey "improbable."
Robertsdale, located near Alabama's Gulf Coast around 25 miles from Mobile, is overwhelmingly white, has a population of 5,000 and a median household income of $40,000, according to city-data.com.
Cupertino, in the heart of Silicon Valley, is ethnically diverse, has 50,000 residents, and has a median household income of $120,000.
"I am where I am in life because my parents sacrificed more than they should have, because of teachers, professors, friends and mentors who cared more than they had to, and because of Steve Jobs and Apple," Cook said last year at Auburn.
Those who live in Robertsdale describe it as a typical Southern farming town, close-knit and crazy about football, a place where the high school is the center of activity.
Cook was the middle of three boys in a family described by people in Robertsdale as just "real nice." His parents, Geraldine and Donald, have become local celebrities of a sort, as their son's star has risen out in California.
A local TV affiliate ran a feature segment on the Cooks in 2009. Donald Cook, who is retired and bears a striking resemblance to his son, told the camera that Tim calls home every Sunday morning without fail.
"I never even dreamed that Tim would be where he is today," Geraldine Cook said in the segment.
At Robertsdale High School, Cook finished No. 2 in his class of roughly 175 students in 1978, was president of the National Honor Society, played in the band, and was voted "most studious," according to the yearbook.
Cook earned a degree in industrial engineering from Auburn in 1982, and received his MBA from Duke University in 1988.
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