On Friday, BoomTown first reported that new Yahoo CEO Carol Bartz is likely to be announcing a sweeping new management structure soon, which can only mean the possibility that some existing top execs are likely to be broomed out, even as some new ones are ushered in.

“This is going to be a full-scale peanut butter recall,” joked one exec, referring to the infamous “Peanut Butter Manifesto,” which was sent around the company several years ago by former exec Brad Garlinghouse. It laid bare the problems at Yahoo (YHOO), most especially a decided lack of decision-making and lugubrious levels of managers.

But the reorganization of Yahoo’s top-heavy management structures–I once dubbed it the “attack of the Yahoo vice presidents”–will be a bit sticky, given all the (slow-)moving parts at Yahoo (YHOO).

Nonetheless, Bartz signaled a “big week” ahead in one internal memo I obtained, which was sent out Friday.

So what’s to come?

Here’s a rough primer, based on talking to numerous sources inside and outside of Yahoo:

The Basics:

In order to start to revive Yahoo, Bartz is likely to impose a more top-down management style on the hopelessly confusing “matrix” organization now in place at the company.

She has spent the last six weeks touring Yahoo, getting to see a lot of presentations on its many, many products and conducting a whirlwind of meetings with execs.

Broadly, most expect Bartz to severely roll back a variety of previous reorganizations done by former CEO Jerry Yang and outgoing President Sue Decker, in order to impose more centralized control over the place and focus it more narrowly.

Presumably, lattes–paid for by Yang and co-founder David Filo–will remain free.

Out With the Old:

There’s no question that Yahoo is going to see the departure of several top execs, along with the elevation of others.

Among those who are more likely to be definitely in, though, is CTO Ari Balogh (pictured here), a relatively recent hire who has been a popular exec within Yahoo.

The Wall Street Journal first noted the possible rise of Balogh in a follow-up piece to this column’s story on the overall reorg over the weekend, noting that he would become head of product.

Presumably, Balogh will be one of the point men on what to do about search, in the should-I-stay-or-should-I-sell-now debate that never seems to end at Yahoo.

One interesting idea floating around Yahoo is that he becomes head of all its products, as well as continuing to run its tech arm.

That’s a good idea, since Yahoo has desperately needed an empowered leader under Bartz, who focuses like a laser beam on products.

“It all starts with that,” said one former exec. “One single person has to be the champion of what Yahoo makes.”

But what does that mean for Ash Patel, EVP of Yahoo’s Audience Product Division? Well, the longtime Yahoo veteran could now report to Balogh (he had previously reported to Decker directly) or, presumably, leave.

Patel’s fate, of course, impacts that of many others, such as Front Doors head Tapan Bhat, who is in charge of a major homepage redesign that Bartz just delayed the launch of to make it better.

Venkat Panchapakesan, EVP of the Audience Technology Group, seems safer, given that he reports to Balogh already and is responsible for the company’s overall product technology and platform strategy, such as its open efforts.

Also safer than not is General Counsel Michael Callahan, as well as U.S. EVP Hilary Schneider.

But Schneider’s purview might change a bit if U.S. advertising sales head Joanne Bradford–who now reports to her–is elevated to a higher position or if sales is taken out from under Schneider.

It’s not a stretch to imagine Bartz wanting more control of the part of Yahoo that brings in the bucks.

The fate of Connected Life Division EVP Marco Boerries is dicier–think Yahoo mobile and other devices–as it is for CFO Blake Jorgensen and David Windley, who heads human resources.

Both Jorgensen and Windley were favored by Decker, which does not necessarily make them goners. But both are in jobs on which Bartz will have to rely much more, so she might want her own choices in place.

Boerries (pictured here), a talented but more freewheeling exec under Yang, is another question all together. Already wealthy from selling several companies, the entrepreneurial exec is most often mentioned by sources as someone unlikely to stick around, especially if Bartz tries to rein him in more. (In addition, Boerries has family issues requiring that he spend a lot of time in his native Germany.)

As to the many Yahoo SVPs and VPs? Let’s just say it is likely there will be many fewer of them, as Bartz cuts, consolidates, simplifies and centralizes divisions more.

In With the New:

One hire that is definitely coming is a new chief of marketing to take over Yahoo’s brand, as well as its PR function. Yahoo has not had that kind of powerful exec in a long time, and it is more likely Bartz will go for an outside star here.

One outside name skittering around Yahoo for the role is John Vail (pictured here), director of interactive marketing for Pepsi-Cola North America, who knows Yahoo well.

(An obvious internal candidate for the job would be Yahoo’s Global Brand Marketing SVP, Allen Olivo, who could hit the road if not selected.)

Also a possibility is adding a COO with more Web experience to come in to help Bartz. There are plenty of candidates for that job all over the Internet sector.

But Bartz seems to be the kind of exec who favors flying solo and having key execs report to her to keep a finger on the pulse of a company. She is most definitely not going to have an entourage around her.

In fact, said one person familiar with the situation: “It’s long past time for new plumbing, and [Bartz] seems ready to flush a lot out that has long needed to go.”

My favorite anecdote collected so far about new Yahoo CEO Carol Bartz is the one in which she recently called together two separate groups of execs who were direct reports of former Yahoo CEO Jerry Yang and President Sue Decker.

Bartz, several sources recounted, went around the table and asked them one by one what they actually did, making various outspoken comments along the way.

Two execs, for example, were a “two-in-one box,” meaning they did the same thing to her mind. And she had to get well around the room until she could find someone who made some dough. “Finally, revenue,” Bartz reportedly joked.

Stories about Bartz’s take-charge style have been ricocheting through Yahoo (YHOO) and outside it too, which is probably just what the tough-talking veteran exec has been aiming for as she navigates the troubled company to come up with a plan to revive it.

And despite all the jokes about Yahoo’s proclivity to constantly rearrange deck chairs, most expect Bartz to launch a significant reorganization as soon as she is up to speed. Which might be very soon indeed.

But of all the various things many employees I have talked to hope she does first is dump the “matrix” and replace it with a much simpler management system where top execs are more directly responsible for their P&L and less with complicated cross-functional corporate hairballs.

Ah, the dreaded matrix of Yahoo–that much maligned organizational structure that was instituted at the company under the reign of then-CEO Terry Semel and complexified drastically under Yang and Decker.

How to explain the matrix, whose goal was to simplify the huge global behemoth that is Yahoo by having a lot of managers over employees working on similar products?

Simply put, shared ownership, presumably, would make the troops of Yahoo work better across geographies.

There are pluses explained one exec: “The theory behind all of this is that if you centralize the functions you can share resources across various projects….Some degree of centralization is absolutely appropriate at big companies. You don’t want each business unit having its own finance or legal people, for example.”

But that also removes a lot of critical tools from line managers, many said, putting them into a larger pot where many are cooking.

Thus, the matrix has come to symbolize a drastic lack of accountability at Yahoo.

And, more to the point, a horrible gridlock in decision-making, which has stopped it from moving quickly in the face of more nimble and, let’s be honest, more dictatorially-run companies–think Apple’s (AAPL) Steve Jobs or Facebook’s Mark Zuckerberg and you have a good idea what I mean.

Said one exec who has left the company about the downside of the matrix: “The great people leave because they don’t feel they have the tools and authority to be successful with what they are notionally responsible for. Or because there are so many people who think they are in charge, they can’t get anything done. The mediocre people stay as they are protected and not held accountable.”

Said another still there, in what is the more prevalent opinion of more than a dozen people I spoke to: “I hope Bartz takes the blue pill and we can forget all about the matrix.”

It’s a reference to the movie, “The Matrix,” in which the hero, Neo, is given a choice by Morpheus between a red and blue pill.

Says Morpheus: “You take the blue pill, the story ends, you wake up in your bed, and believe whatever you want to believe. You take the red pill, you stay in Wonderland, and I show you just how deep the rabbit hole goes.”

Many at Yahoo, by contrast, are hoping the days of rabbit holes are finally over.

In any case, until Bartz acts, here’s the cool red pill/blue pill scene from “The Matrix”: