One of my favorite elements in Adam Lashinsky’s How Apple Works — the “inside” story that created a sensation when it appeared in the May 23 issue of Fortune but was made fully available online only last week — was the organization chart assembled by Fortune‘s graphics team under the guidance of senior research editor Doris Burke. (Click to enlarge the high-res version at right.)

It’s a bit out of date. Retail chief Ron Johnson, for example, announced in June that he was leaving for J.C. Penney (JCP).

But now the chart is about to change in a more substantive way, and how Apple (AAPL) reorganizes itself under Tim Cook  is one of the central issues the company faces in the post-Steve Jobs era.

Jean-Louis Gasseé, in a “Monday Note” entitled Steve: Who’s going to protect us from cheap and mediocre now?, suggests that Cook’s name will move to the center. But it’s not going be that simple. Tim Cook is not Steve Jobs, and he’s the first to admit it.

“Come on, replace Steve? No. He’s irreplaceable,” Cook is quoted as saying in Lashinsky’s 2008 Fortune profile The genius behind Steve. “That’s something people have to get over.”

So what kind of organization will Cook create? His official bio on Apple’s leadership page offers some clues:

Before being named CEO in August 2011, Tim was Apple’s Chief Operating Officer and was responsible for all of the company’s worldwide sales and operations, including end-to-end management of Apple’s supply chain, sales activities, and service and support in all markets and countries. He also headed Apple’s Macintosh division and played a key role in the continued development of strategic reseller and supplier relationships, ensuring flexibility in response to an increasingly demanding marketplace.

As John Gruber suggested in Friday’s Talk Show podcast (That day has come), if you showed the list of Cook’s responsibilities as COO to someone who didn’t know anything about Apple and asked them guess his title, most people would probably assume that Cook was already CEO.

But take note of what’s missing. Cook did not oversee Apple’s industrial design — that was Jony Ive answering directly to Jobs. Or its iPhone and iPad software division — that was Scott Forestall answering to Jobs. Or marketing (Phil Schiller). Or retail (Ron Johson). Or Internet services (Eddy Cue).

What this suggests to me is that a year or so from now, Apple may have evolved from a spoke-and-wheel organization into a more traditional, top-down pyramid.

In the new org chart, Cook’s name would be at the top, to be sure. But below him would be arrayed the names of the vice presidents who have risen in the organization as they assumed more control and independence than they ever had under Jobs.

But this is only speculation. Perhaps Doris Burke and her graphics team will someday show us how it really turned out.