Rivals for corporate control playing King of the Mountain

This is the time of year when the corporate dirty linen gets hung out for shareholders to look over. It's proxy-fight season. With annual meeting season heading for a peak, a score of proxy fights - battles to control shareholders' votes - are going on. Among them are:

* GAF Corporation vs. GAF Shareholders' Committee for New Management. In this battle, a dissident shareholder, Samuel Heyman, a Westport, Conn., developer of shopping centers, is seeking to oust GAF's management. He alleges that one of the directors has testified in court to having made illegal payoffs to a union official who was later convicted of extortion. Mr. Heyman also charges that GAF chairman Jesse Werner mismanaged the company for his own benefit by selling off assets to stay in business.

GAF, for its part, says Mr. Heyman is making ''malicious, unfair, and distorted personal attacks. . . .'' In the meantime, GAF has announced plans to sell off one of its largest subsidiaries.

* TW Corporation vs. Odyssey Partners. This contest pits TW Corporation, the holding company for Trans World Airlines, against some of the former partners of Oppenheimer & Co. Odyssey wants TW to spin off its primary subsidiaries, distributing the proceeds to the shareholders. Odyssey contends that ''the sum of Trans World's parts would be greater than the whole.''

TW's response is to note that Odyssey Partners' projections are based on ''hypothetical assumptions,'' including those of earnings. In an unusual development, Odyssey hired Booz, Allen & Hamilton, a management consulting firm, to analyze its plan.

* Louisiana Land & Exploration vs. the Louisiana Land Committee for New Management. Led by Delo H. Caspary, who operates an oil service and supply company in Rockport, Texas, a group of nine businessmen is pressing for a change of management at Louisiana Land. It claims Louisiana Land's management is ''dismal.'' In the dissident group's own proxy material, it quotes from an article in Forbes magazine which said the company should sell at a discount because of its management - not a premium.

It is believed the Hunt family, which owns a large chunk of the company, is in favor of the dissident group. Louisiana Land management, in its proxy and in public comments, has said little about the proxy fight.

* Canal Randolph vs. Asher B. Edelman, et al. Mr. Edelman, who is involved in the arbitrage securities business, wants to replace Canal's board with what he considers ''experienced domestic businessmen and community leaders.'' He claims Canal has stacked its board with foreign board members who have little interest in the company's affairs.

The company, for its part, notes that Mr. Edelman's board nominees only recently became shareholders of the company and are funded by Mr. Edelman. Mr. Edelman appears to have made about $6 million on the stock's run-up so far.

There are similar fights every spring. John J. Gavin, executive vice-president at D.F. King & Co., one of the largest proxy solicitation firms, says, ''We have the shareholders manifesting their dissatisfaction with the performance of management or the proposals put forth by management.''

Or, as Richard B. Nye, president of Georgeson & Co., notes, shareholders often have their own proposals. This is so with Mr. Heyman, who is proposing that GAF sell its specialty chemicals division and stay in the roofing materials business, which the company is trying to sell.

Most of the time management wins. Mr. Gavin, an 18-year veteran of proxy wars , explains that ''when you have a proxy fight you attempt to get the shareholder to say his investment decision was wrong. This is a hard thing to accomplish.'' In addition, dissident shareholders often have a hard time putting together a credible board of directors.

One of the first moves a company makes is to hire a law firm that specializes in takeovers and proxy fights. TW Corporation, for example, has hired Wachtell, Lipton, Rosen & Katz. Louisiana Land has hired Skadden, Arps, Slate, Meagher & Flom. Such firms regularly become involved in takeovers and mergers and have built up reputations for their astuteness or combativeness.

Once a law firm is hired, the next step is to hire a proxy solicitation firm. The competition among these firms is fierce. Some of them will represent only management. Others are ''hired guns,'' and will represent anyone with cash in hand.

For the most part the proxy firms work by mailing management's positions to the shareholders. According to Securities and Exchange Commission rules governing proxy contests, however, the opposition has the right to a list of shareholders and can likewise make such mailings. As the deadline for the annual meeting approaches, the proxy firms work late into the night, calling shareholders. ''You don't call at dinner hour,'' Mr. Gavin says, ''and you try not to antagonize people. You have to understand human nature.''

The proxy solicitation business is getting increasingly computerized. Kenneth Altman, an energetic vice-president at Hill & Knowlton, which is best known as a public relations firm, says H&K has computerized the proxy business so it knows at any given moment which institutions have voted with management and which haven't. Also, he says, computerization allows the firm to analyze where a company's shareholders live. Thus, the company can gear its advertising to the markets where the shareholders are.

Of particular importance is the stock held by the big brokerage houses in ''street name.'' Stock held in street name is held by a bank or stockbroker for an unnamed client. Reaching the shareholders who have their stock held by the brokers is difficult, prompting some of the solicitors to concentrate on the institutions holding large amounts of stock.

The proxy solicitation firms for both sides telephone shareholders right up until the last minute. ''In theory,'' Mr. Gavin says, ''you want to be the first to get in touch with the shareholders and the last to contact them.''

This year, in an effort to thwart some of the takeovers that have been occurring, companies are trying to use what Forbes has termed ''shark repellent, '' or amendments to the company's bylaws.

This year various amendments include hiring a staggered board by electing a third of it every year; requiring the acquiring companies involved in so-called two-tier takeovers to pay the same amount to the second set of shareholders as to the first set; and requiring a ''super majority'' to force a board meeting.