Hard on the heels of Paul Henze's The Plot to Kill the Pope (K 1983, p. 1119) comes this much better-documented account--which makes the case for Bulgarian-Soviet backing of Mehmet Ali Agca look like an intuitive certainty. Sterling is a veteran Rome-based journalist whose Sept. '82 Reader's Digest article on the attempted assassination of John Paul II helped to fuel what she saw as suspiciously lukewarm Western concern over the whole affair. The picture she draws is complex but basically clear: Agca is neither crazy (psychiatrists found him cool and self-possessed) nor an inveterate liar (his confession to Judge Ilario Martella was full of solid information), and he obviously had extensive dealings with the Bulgarian secret service. The Bulgarians have long cultivated friendly ties with the Turkish Mafia, which they used as a pipeline for shipping contraband into Turkey (especially munitions, to destabilize the battered country) and drawing heroin out (to he sold in the West). Whoever first selected Agca as a gunman, Turks and Bulgarians cooperated in building him up as a right-wing fanatic, whence his strange self-incrimination for the murder of left-wing editor Abdi Ipekci and his even stranger escape from the super-security Kartal-Maltepe prison while under sentence of death. Somebody supplied Agca with a first-rate false passport, $50,000, and training in terrorism, and the evidence points directly at--among others--Sergei Antonov, deputy director of Balkanair and a Bulgarian agent. No one seriously doubts that the Bulgarians take their orders from the KGB, and the Soviets had powerful reasons for wanting the Pope out of the way. The only real enigma is why the CIA and BKA (West German police) have shown so little interest in the investigation. Judge Martella's upcoming report to the Italian Prosecutor General's Office will probably not bust the case wide open, and a smoking Soviet gun isn't apt to turn up; but Sterling's legwork and detailed presentation seem to have gotten the goods on the ""Bulgarian Connection."" Fascinating and, necessarily, disturbing.