One of the big questions left unanswered in President Anwar Sadat's recent reorganization of Egypt's government and political structure is: Who owns the newspapers?

Under a 1961 law, the Arab Socialist Union, which was Egypt's only legal political organization, owned a majority interest in the publishing houses that print all the country's major newspapers and magazines.

Sadat, however, has legalized political parties and abolished the Arab Socialist Union, leaving the ownership of the papers up in the air and setting off a national debate about what should be done with them.

As chairman of the Arab Socialist Union, Sadat had the power to appoint the editors and board chairmen of the publishing houses, which gave him effective control of the papers and their contents. It is not clear who has that authority now.

Nor is it clear who exercises economic control over the publishing organizations, which do more than print newspapers.

One of them, the A1 Ahram organi-American communications conglomerate by acquiring a commercial print shop, and advertising agency, a micro-film and computer center, an interest in a ballpoint pen factory and a near-monopoly over the import of foreign language newspapers and magazines.

The degree of press freedom has been a political issue in Egypt for more than a century. Sadat, a former journalist, has wrestled with it throughout this eight-year presidency.

His declared policy is that the press is free but must exercise responsibility in the national interest. In practice, that has meant lively debate and criticism over internal issues such as public services, but docile adherence to the official line on matters of foreign policy, natioanl security and the military. Writers and editors who stepped over the undefined boundary, particularly those on the left, have been fired or silenced.

There are a handful of independent publications. The Moslem Brotherhood, banned under Sadat's predecessor, Gamal Abdel Nasser, puts out a monthly magazine that has been tolerated despite its regular criticism of Sadat's policies. A bland French-language daily remains in private hands.

But all the major newspapers and magazines were operated under basically the same structure - 49 percent of the assets collectively owned by the staff, who shared in any profits, and the other 51 percent by the Arab Socialist Union.

Sadat has said he is determined to keep majority control in some collective organization and out of the hands of individuals, but no new system has yet been developed.

Sadat says he wants the press to become a "fourth authority" in Egypt, alongside the executive, legislative and judiciary authorities, but he has not made clear what he means by this.

"We don't yet know what the outcome will be," said Ali Hamdi Gamal, editor-in-chief and chairman of the board of A1 Ahram.

"With the abolition of the ASU, we have to figure out what our status is. The president has said he wants to make the press the fourth authority of the state, but how? This is all under discussion."

Within each publishing organization, the journalists and craft workers such as printers have been holding meetings to talk about what new system they want to replace the old one.According to some of the participants, the discussions have been especially heated a among the editorial staffs, where younger journalists are pressing for more freedom to write about sensitive subjects.

According to Gamal, the results of these meetings will be sent to the parliament, which is dominated by Sadat's own National Democratic Party, for consideration when parliament drafts its new regulations on the press.

Some of the proposals that have been put forward, such as allowing the staffs to select the editors-in-chiefs, would remove a powerful prerogative from the president.

Gamal said he thought Sadat might accept that because "he is adamant in wanting to guarantee freedom of the press. I believe the journalists will be satisfied with their future."