Just before New Year, Hewlett-Packard Co. (NYSE: HPQ), the world’s No. 1 computer maker, filed a document with the U.S. Securities and Exchange Commission acknowledging it’s evaluating asset sales.

The move was more than 14 months after new CEO Margaret (Meg) Whitman cancelled a proposed sale of the PC division, then the world’s largest, not long after the $11 billion acquisition of Autonomy, a UK specialist in unstructured search and multimedia.

In October, Whitman conducted an “investor day,” in which she and CFO Cathie Lesjak said they needed to take huge charges, lay off thousands and whip the Palo Alto, Calif., company back into shape, warning it would take two years.

Then they reported a record annual loss for the year ended Oct. 31, followed in November by a near-total write-off of the Autonomy purchase, coupled with charges of fraud, which are under investigation by the FBI, the U.S. Department of Justice and the UK Special Fraud Office.

Former Autonomy CEO Mike Lynch decried the charges outright.

The latest SEC filing merely states the company “continues to evaluate the potential disposition of assets and businesses that may no [longer] help us meet our objectives.” That’s helped send HP shares up nearly 6 percent in a week. They closed Friday at $15.14, unchanged.

Since Whitman’s been HP CEO, the shares have declined nearly 36 percent.

Analysts, including Steve Milunovich of UBS, have called for months for Whitman to cut the company in half: One side would be the PC unit, now No. 2 worldwide, with the printer business, No. 1 worldwide. Whitman combined them in one of her first consolidations.

That would create what might be called “HP Consumer” and could conceivably include innovations, such as a smart phone, entertainment products and other office-related devices.

The other part might be “HP Professional,” which would encompass HP’s sophisticated servers, software and middleware, professional services and its networking lines like the former 3Com that compete against Cisco Systems Inc. (NASDAQ: CSCO).

Given that HP’s market capitalization now is a mere $29.8 billion, the split might be encouraging, although it would create enormous costs, be disruptive and could fail. Under prior management, HP divested its original instrument business, now Agilent Technologies (NYSE:A); semiconductor lines, now Avago Technologies (NASDAQ: AVGO) and other units including Octel Communications, a PBX company.

Rather than radical surgery, Whitman and Lesjak might want to sell off pieces of the company, such as Palm, the owner of the WebOS that was installed in the ill-fated TouchPad of 2011, or parts of Electronic Data Systems that don’t meet targets for growth.

“We think expectations for a recovery in most of HP’s core-end markets remain bleak and at most several years away,” said Angelo Zino of Standard & Poor’s. Rather than split apart, he said, the company is more likely to trim down, improve cash flow and then “prove it’s on the right track” after so many missteps by management.

Another huge minefield: pension fund liabilities for the company’s 331,000 employees.

Milunovich estimates the pension plan for the year ended Oct. 31 was underfunded by $5 billion. Still, if management were to handle it as with the employees in the Agilent spin-off, it could be done.