When the feds nailed John Gotti earlier this year, they decapitated a crime syndicate that, according to Davis (Mafia Kingfish, 1988, etc.), numbers perhaps 500 ``soldiers'' and thousands of associates, and nets at least $500 million annually. How the Gambino crime family reached this dark pinnacle makes, in Davis's hands, for a gripping true-crime history. As in his other dynastic studies (The Kennedys, 1984, etc.), Davis doesn't dig out new data here so much as collate others' research, spiced with his own firsthand anecdotes. Though the roots of the Gambinos, he explains, reach back to the Neapolitan and Sicilian mobs of the early 1900's, the crime family's story really begins in 1931, when Lucky Luciano reorganized New York's underworld and named one Vincent Mangano to head the most powerful faction, or family. In 1951, Mangano was killed, probably by Murder Inc. head Albert Anastasia, who took over as family boss; Anastasia's underboss was Carlo Gambino, who, in 1957, engineered his chief's murder and became boss in turn, giving the family its name. Davis focuses on the reigns of Gambino, the ultimate mob businessman, bland but ruthless; his successor, Paul Castellano, who ruled like a caesar from his Staten Island mansion; and Gotti. The author covers every rumor and fact about the Gambinos (e.g., that J. Edgar Hoover kept hands off organized crime because he got betting tips from Gambino Çminence grise Frank Costello). Davis describes his encounters in Naples with the exiled Luciano (``a small man with narrow sloping shoulders and a repulsive face''); offers an eyewitness account of the recent Gotti trial; and explains the economic workings of the family in full. He also—in the book's primary flaw—envelopes his text in moral thunder (Carlo Gambino was ``a monstrous parasite,'' etc.). An authoritative overview of the nation's premier criminal organization, and of the greed and hubris that have toppled its leaders time and again. (Photos—16 pp.—not seen.)