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In the fall of 2001, Hewlett-Packard announced a momentous $25 billion merger with Compaq.

“This is a decisive move that accelerates our strategy and positions us to win by offering even greater value to our customers and partners,” declared Carly Fiorina, HP’s chairwoman and chief executive at the time, describing how the deal would “create substantial share owner value.”

Thirteen years later, just this fall, Meg Whitman, HP’s current chairwoman and chief executive, undid that deal, splitting the company in two. “It will provide each new company with the independence, focus, financial resources and flexibility they need to adapt quickly to market and customer dynamics.”

Eerily mirroring Ms. Fiorina’s words, she said the divorced companies “will be in an even better position to compete in the market, support our customers and partners, and deliver maximum value to our shareholders.”

So which was the right decision? The merger or the spinoff?

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The current deal-making boom has been filled with headline-grabbing mergers. At the same time, corporate America is spinning off assets by the truckload.

The numbers tell the story: Through last month, global merger activity had surpassed $3 trillion, according to Thomson Reuters. At least 28 large companies like eBay and HP are pursuing spinoffs or divestiture plans, according to Credit Suisse. That is more than any other year in the last decade.

All of which leads to the all-important question swirling in the boardrooms of corporate America: Who is creating more value? Is the bigger-is-better crowd right? Or is the smaller-and-more-focused pack the one to follow? And is the premise of the question even correct? Is it an either-or proposition?

Mergers have a spotty record of creating value. Putting two companies together is risky. Take your pick from dozens of academic studies and the consensus is that mergers destroy value at least half of the time, to the point that it’s almost become a cliché. But when mergers are timed right — usually during a downturn in the market — and executed properly (usually with smaller acquisitions), much value can be created.

Spinoffs and divestitures, however, are usually a much better bet. The studies repeatedly show that spinoffs and divestitures create value both in the short and long term. Some studies show that companies that are involved in a spinoff outperform the market by 15 to 30 percent over three years. Even the announcement of a spinoff seems to push stock prices higher. According to the Boston Consulting Group, “55 percent of all divestitures created value, as measured by the average cumulative abnormal return” over seven days.

Of course, it is an axiom in the deal-making game that companies go through buildup cycles only to later tear down. Rinse and repeat. Of course, the armies of bankers and lawyers involved in these deals — often orchestrating an acquisition and its eventual divestiture — command huge fees along the way.

If many large-scale deals end in a divestiture, why make the acquisitions in the first place? And why are companies typically so slow to pursue spinoffs?

“Divestitures and spinoffs are the ugly stepchild of corporate strategy,” Emilie R. Feldman, a professor of management at the Wharton School at the University of Pennsylvania, declared provocatively on one of the school’s radio programs. “They are viewed as acknowledgments of failures, bowing to pressure from investors and competitors. In reality, spinoffs can be used very proactively, as we are seeing in the HP case, to create value for shareholders and separate businesses that don’t belong together anymore.”

The problem, of course, is that dismantling an earlier transaction requires a certain kind of courage to admit that the original deal might not have worked as well as expected — or at least isn’t working anymore.

John Donahoe, eBay’s chief executive, decided to spin off PayPal after nearly a year of resisting Carl C. Icahn, the activist investor who had been pressing for such a deal. Originally, Mr. Donahoe argued that “the best way to drive long-term shareholder value is to keep eBay and PayPal together, to capitalize on the opportunities,” contending that “the distraction and dis-synergies of separation would be happening exactly at the wrong time.” Six months later, after having settled a proxy contest with Mr. Icahn, Mr. Donahoe said the time was right for a spinoff. Not much had changed except Mr. Donahoe and eBay’s board would not look as if they were knuckling under the pressure of an activist investor.

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Ms. Whitman, too, took her time to unwind the mishmash of businesses that HP had become. The previous chief, Léo Apotheker, had tried to dismantle the company three years earlier. When Ms. Whitman was selected to run the company, she announced that the company needed to remain together, arguing there was more value that way. The payoff never materialized, and she ended up dividing the company.

In both cases, though, it was easier for Mr. Donahoe and Ms. Whitman to break up their companies because they were not the founders, nor were they responsible for the original acquisitions.

When Procter & Gamble recently sold its Duracell unit to Warren Buffett’s Berkshire Hathaway for $4.7 billion, there wasn’t much sentimental debate or hand-wringing in the executive suite about it, in part because it had come along as a unit of Gillette, which P.&G. had acquired in 2005 for $57 billion.

The divestiture of Duracell is just another round-trip of sorts for the company. It had been owned by Kohlberg Kravis Roberts before it was sold to Gillette for $7 billion in stock in 1996. Mr. Buffett appears to be buying the business nearly two decades later at a discount. When Gillette acquired Duracell, it planned to use its heft to sell razor blades and batteries at the front of the store.

“The checkout counter, there is going to be nobody that can touch what we can do,” Gillette’s chief executive said at the time. As part of P.&G., however, the business was less relevant and didn’t give the consumer giant any additional leverage it didn’t have on its own.

More spinoffs are expected. Credit Suisse put out a list of possible spinoffs that could soon be making headlines. It included IBM, Oracle, Black & Decker and General Electric.

Spinoffs are attractive, in part, because they are tax-free to investors. Selling a business directly to a rival is considered a taxable event.

But another trend may start developing in about two years. Mark your calendar: Many of those companies that are being spun off now could very likely be gobbled up all over again by rival companies. Why two years? After that time, lawyers say, such deals are tax-free.

This reassembling phase is best illustrated by AT&T. After the government forced the company to break up into various pieces, the so-called Baby Bells essentially reunited a big chunk of AT&T through acquisitions.

Consider this all just part of the circle of life of the mergers and acquisitions world.

Bruce Wasserstein, the legendary deal maker, once wrote: “Over the years, the rationale, style and intensity of successive merger waves have varied, and a rich assortment of knaves and fools, heroes and winners, have played cameo roles.”

But who is the knave and who is the hero remains the question, because often they are both.