Sons Inherit a Debt-Strapped, Complex Empire SUBS third graf to UPDATE estimate of entire worth; PICK UP 4th graf, In what ...

LONDON (AP) _ Two of Robert Maxwell's sons took control of his businesses Tuesday after the magnate's death at sea, inheriting a debt-swamped tangle of companies that might have to be further dismantled to satisfy bankers.

The boards of Maxwell Communication Corp. PLC and Mirror Group Newspapers PLC appointed the sons as acting chairmen when word first broke that their billionaire father was missing from his yacht near the Canary Islands.

Maxwell already had begun selling companies to reduce Maxwell Communication's $3.1 billion in debt, which doesn't begin to come due for a year. The Financial Times, in an analysis in its Wednesday editions, estimated the entire empire's debt at $4 billion.

In what stock analysts called an ironic twist, the two companies' shares, depressed by worries about the debt, could rise sharply when they resume trading on Wednesday.

Trading in the stock of both companies was suspended during the search for Maxwell, freezing the price of Maxwell Communication at 122 pence, or $2.16 a share, and of Mirror Group at 77.5 pence, or $1.37, on the London stock exchange.

''In a curious way, it (Maxwell's death) may have a beneficial impact,'' said Peter Checketts, financial editor of the newsletter European Media Business and Finance.

''Maxwell has always suffered from the 'Max Factor,' which has arisen because of his unpredictable nature and the fact that he's basically a bully,'' Checketts said. ''The share price for MCC has reflected that.''

Derek Terrington, a media analyst with the London investment firm Kleinwort Benson Ltd., said: ''You must see it as a fresh start for the companies. You must see it as an optimistic tack.''

Maxwell's son Ian said outside the Mirror Group headquarters near Fleet Street that Maxwell's death was ''very sad news'' for the family and the companies' employees and shareholders.

Maxwell's companies, which employ more than 15,000 people, were continuing to operate, Charles Wilson, editorial director of the Mirror Group, said in a telephone interview.

''Everyone in the company, from the boardroom level down, has been traumatically shocked,'' Wilson said.

However, he said Maxwell was on leave when he disappeared, and he noted that Maxwell's sons have been working in the family business, which has other operational managers as well.

''The company was being run in his absence anyway,'' Wilson said. ''The only confusion is as to where and when he disappeared.''

The highly complex Maxwell empire was divided into three main groups.

Maxwell Communication, publicly held but Maxwell-controlled, owns the book and encyclopedia publishers Macmillan Inc. and P.F. Collier. It also owns the Official Airline Guides, Prentice Hall Information Services and Berlitz language schools.

Maxwell's Mirror Group, 49 percent of which Maxwell sold on the London stock market in May, publishes the Daily Mirror, Britain's second-largest newspaper with a circulation of 2.9 million, and four other British newspapers.

Maxwell's private interests are grouped under Robert Maxwell Holdings Ltd. They include the New York Daily News, which Maxwell bought from the Tribune Co. in March and The European, a weekly English-language newspaper distributed across the Continent.

Further complicating matters, the Liechtenstein-based Maxwell Foundation, a charitable trust, owns stakes in the Maxwell companies.

Derek Brock, a media analyst with Nomura Research Institute, said: ''We know very little of the financial structure of the family interests. It's very difficult to know just what assets there are, and where they are, and what are the debts of the various companies.''

Maxwell had accumulated the debts building up a publishing empire after turning away from printing. He encountered trouble when interest rates rose and the recession set in, vastly raising his carrying costs at a time when advertising in newspapers was falling.

The boards on Tuesday named Maxwell's sons Kevin, 32, as acting chairman of Maxwell Communication, and Ian, 35, as acting chairman of the Mirror Group. The sons have been joint managing directors of Maxwell Communication since 1988.

Checketts said: ''He's been grooming his sons for succession. They seem pretty able managers but fairly inexperienced.''

Maxwell historically retained control of his companies, and he was a mercurial hands-on manager, until his attention was diverted to a new project.

''It's going to be a challenge for his children,'' Checketts said, ''He basically left the boat in deep waters.''

Maxwell Communication has a payment of $750 million due in October 1992, and of $1.25 billion in 1994.

''They'll (the sons) probably consolidate and merge his activities and we might see some disposals,'' Checketts said. The American businesses are the most likely sale targets, analysts said.

Maxwell announced in July he wanted to spin off the U.S. businesses of Maxwell Communication into a separate public company.

He sold Pergamon Press PLC, the foundation of his empire, to the Dutch company Elsevier N.V. for $779 million in March.

Maxwell Communication earned $86.4 million on sales of $1.89 billion in the year ended March 31.

The Mirror Group earned $66 million on revenue of $788 million in 1990.