Two years after the shooting of Pope John Paul II, the torrent of accusations implicating Bulgaria and the Kremlin itself has subsided into an eddy of theories, political and diplomatic machination, and prolonged anticipation of results of Italy's investigation.

Only one taciturn man knows whether a convincing case exists for what the Italian media has dubbed the "Bulgarian connection." He is Ilario Martella, the investigating magistrate empowered to probe the sometimes-questionable allegations by the Turkish would-be assassin Mehmet Ali Agca that he received help from imprisoned Bulgarian airline official Sergei Antonov.

Interviews with government officials and other sources familiar with the case during a three-week journalistic inquiry in Italy, Turkey, Bulgaria, Switzerland and France suggest that the Italian magistrate has gone furthest in the investigation. Martella has a reputation for probity, and a higher court that has considered submissions from him and Antonov's lawyers twice has upheld the Bulgarian's detention.

But Martella, who legally has up to 5 1/2 years before deciding whether to send Antonov to trial, may choose to take until early next year to present his case, according to Italian sources. Meanwhile the magistrate, other Italian officials and even the U.S. Embassy here have clamped heavy secrecy on the investigation. They were troubled by leaks and charges at the end of last year over findings regarding Antonov and two other Rome-based Bulgarian employes charged in the case.

As a result, little is known of how much independent evidence supports the hypothesis that Bulgarian intelligence officers plotted to kill John Paul on behalf of the Kremlin because of the pope's support for the Solidarity union in his native Poland. A variety of non-Communist intelligence agencies, reportedly including those of Turkey, Israel and major western powers, are not yet convinced that the Bulgarians were behind the plot.

Agca, presented with a file of photographs, has picked mug shots of the three Bulgarians with whom he supposedly planned the May 13, 1981, shooting. He also described Antonov's apartment after saying that he met there with them.

In his description, however, Agca mentioned having seen a folding wooden door that in fact was present in other apartments in the building but not in Antonov's, according to Italian sources.

This discrepancy and others have been cited by Antonov's lawyers as suggesting that Agca was fed his information by Italian secret service agents who visited him in jail in autumn of 1981 before the Turk finally began to cooperate in the probe. The Bulgarian and Soviet governments have rejected the charges and suggested that they are part of a smear campaign by western intelligence agencies including the CIA.

The theory of Bulgarian involvement is considered plausible in part because of a pattern of Bulgarian "dirty tricks," particularly in Italy and Turkey, including smuggling of arms, narcotics and support for subversive paramilitary groups.

Statements by Agca have set in motion a parallel investigation of alleged Bulgarian spying in Italy and involvement in a stillborn plot to kill Solidarity leader Lech Walesa during a visit to Rome in 1981.

Months after last fall's burst of publicity, the case today bobs to the surface only occasionally in Italy.

Most officials and other sources are waiting to see if Martella will find some "smoking gun" to tie the investigation together.

The two Bulgarian officials other than Antonov who were charged by Martella are living in Bulgaria and appear unlikely to be extradited. Little has emerged about any possible links between Bulgaria and two Turks jailed by Martella who supposedly provided Agca with his pistol and conveyed an offer of $1.75 million to shoot the pontiff.

Some Italians are convinced that before last year's publicity Martella was counting heavily on the prospect of years of imprisonment to gain more information from those detained.

In Agca's case, at least, Martella's tactics appear to have paid off. Agca first stonewalled with vague testimony and insisted that he acted alone. After serving less than a year of his life sentence, however, he implicated the Bulgarians and fellow Turks in December 1981 and apparently has talked to Martella ever since.

When Agca's statements are compared to challenges by Antonov's lawyers, however, the impression emerges that Agca has not proved infallible.

In addition to noting the nonexistent door in Antonov's apartment, the Bulgarian's lawyers have produced hotel bills indicating that Antonov's wife Rossitska was already in Yugoslavia en route to Bulgaria when Agca said that she was present in the apartment during one of the Turk's meetings there.

The Antonovs' daughter Ani, who also was named by Agca as having been present, was not in Rome at all during that school year but in Sofia.

Antonov's lawyers have intimated that two Italian secret service officials, who are known to have visited Agca in prison, fed false information to him. The lawyers have suggested that the Italian agents may have shown Agca photographs of Antonov and the two Bulgarians whom he later identified for Martella.

It is unclear why the Italian secret services would seek to frame the Bulgarian in this manner. Italy generally has sought to avoid diplomatic difficulties with East Bloc countries, because of its trade ties with them and because of its powerful domestic Communist Party.

How Martella sifts fact from fancy in Agca's outpourings remains unknown. According to Ugur Mumcu, the Turkish journalist who is perhaps the world's leading expert on Agca, the convicted Turk is at heart a relentless publicity hound.

When Martella last February asked Mumcu to accompany him as an official witness in questioning Agca--because of the journalist's vast knowledge of Turkish terrorism and smuggling--the convicted would-be assassin was delighted, Mumcu later recalled.

"He wanted to know what I was going to write," Mumcu said in an interview in Ankara. "He kept comparing himself to Carlos," the alias used by master terrorist Ilyich Ramos Sanchez, who masterminded the shooting of Israelis at the Munich Olympics in 1972.

Martella himself is widely considered to be a thorough magistrate willing to pursue even the slimmest lead. In a country where so many controversies are left to wither in their murky contradictions, he won this reputation for his meticulous handling of the Lockheed scandal in the late 1970s involving bribes that the U.S. aircraft manufacturer paid to leading Italian politicians.

The magistrate is known to have been furious with the leaks that followed Antonov's arrest Nov. 25. Martella reportedly argued that his investigation, roughly comparable to the workings of a U.S. grand jury, had been compromised seriously by the publicity given to the alleged Bulgarian plot.

In his quest for secrecy ever since, Martella has been aided by the U.S. Embassy here, which now refuses to allow its officer in charge of terrorism investigations to meet the press. It apparently fears involvement after journalists, notably columnist William Safire of The New York Times, virtually accused the U.S. Embassy of suppressing evidence of Bulgarian involvement in a quest to preserve good relations between Washington and Moscow.

The reasoning behind these charges was that the Reagan administration could not afford to point an accusing finger at Yuri Andropov, the current Soviet leader who at the time of the assassination attempt was boss of the KGB. The hypothesis of Soviet involvement rests primarily on the assumption that Bulgaria, perhaps the Kremlin's most loyal ally in Eastern Europe, would not undertake such a major task without at least tacit approval from Moscow.

The plausibility of a Soviet-led plot was bolstered by charges in December by Defense Minister Lelio Lagorio that the attack on the pope constituted a "true act of war in time of peace" aimed at providing a "protective and alternative solution to an invasion of Poland."