EDITOR'S NOTE - ''The Mafia this time got too nasty; let's hope it repents and the sacrifice of these martyrs serves some purpose.'' - A fourth-grader's note tacked to a fig tree outside the house of Judge Giovanni Falcone, after a bomb killed the investigator, his wife and three police bodyguards May 23, 1992. Here is a report on what has happened in the year since Falcone was killed.

Undated (AP) _ By FRANCES D'EMILIO Associated Press writer

PALERMO, Sicily (AP) - In this city where so many heroes have died, the hopes of Sicilians, like the towering, shading fig tree, keep growing, fed by the memory of Giovanni Falcone's unflagging determination to wrest his island from Cosa Nostra's centuries-old grip.

So well did he do his job that a year after the blast that killed him on a highway near Palermo, Falcone's legacy is still sending shockwaves, some reaching as far as Rome.

Mafiosi whose trust and respect Falcone won have helped put his colleagues on the trail of suspected ties between the Mafia and leading politicians. The Senate last week voted to lift Giulio Andreotti's parliamentary immunity so Palermo prosecutors can pursue the turncoats' allegations that the former premier met with Cosa Nostra bosses.

And from his last post, in the Justice Ministry in Rome, Falcone designed and then successfully lobbied for laws making it safer for mobsters who want out of Cosa Nostra to come over to the side of the state.

''Pentiti,'' as the turncoats are called, are emerging at the rate of nearly one a day. Their information has led to dozens of raids. One of this new crop of collaborators helped bring about the capture in January of Cosa Nostra's ''boss of bosses,'' Salvatore ''Toto'' Riina - a fugitive for 23 years.

On Saturday, a national squad of Mafia investigators - a group Falcone helped create - probed a car bombing in Rome to see whether it was a rare Cosa Nostra attack outside the mobsters' Sicilan power base. The Friday attack, which injured 23 people, came nine days before the anniversary of the bombing that killed Falcone.

Even after a convulsive year of corruption scandals that have discredited Italy's ruling class, perhaps most important is what didn't happen.

When in 1982, the state's then-top Mafia fighter Gen. Carlo Alberto Dalla Chiesa was gunned down in Sicily, one Palermitano scrawled on a wall: ''Here died the hope of honest Sicilians.''

Now, instead of despairing, hundreds of Palermo's citizens rally every few weeks in front of the courthouse, holding banners cheering on the prosecutors investigating Andreotti.

Such encouragement means a lot to investigators like Leonardo Guarnotta, who works at what was Falcone's desk in a shuttered office with bullet-proof door in Palermo's courthouse.

He and Falcone worked together in the early 1980s, part of a now disbanded team of anti-Mafia magistrates. ''We felt alone,'' Guarnotta said.

Pointing out the popular backing, he ventures: ''Perhaps this is the decisive moment to win the battle'' against the Mafia.

The tree outside Falcone's apartment building is covered with messages scribbled on notebook paper by schoolchildren and stationery by adults.

Bagloads of the messages were sorted through by Falcone's family to make a book called ''The Falcone Tree.'' Sales will help pay for studies of youngsters who want to be magistrates or do police work; enrollment in Palermo university's law department soared after Falcone's death.

Scholarships are meant for children for Palermo's slums, where the Mafia recruit many of their drug dealers, extortionists and murderers.

In a country - and especially in Sicily and elsewhere in the south - where applying for a license to drive or start up a business often depends on connections, Falcone had a different philosophy of working for the state.

He talked often about how ''the powers you had can't be considered a privilege but a means to render a service,'' Guarnotta recalled.

Falcone also was a brave man. Many of the notes pinned on the tree wish the same courage to the investigators of today, shaken further by the death of Paolo Borsellino, Italy's other top Mafia investigator. A bomb killed him and five police escorts on a Palermo street two months after Falcone's death.

''He was a strong man in every sense,'' says Anna Falcone of her younger brother. ''I only heard him voice his fear once,'' in June 1989, after a bomb was found outside his seaside summer house. ''He said, 'I'm a walking corpse.'''

Falcone likely would have savored this moment in which magistrates dare to probe powerful politicians.

''When he came home after (Tommaso) Buscetta testified in court against mob bosses he was euphoric. He thought it was an extraordinary moment,'' Anna Falcone said of the 1986-1987 trial her brother prosecuted. Buscetta, a Mafia turncoat whose testimony has also put American mob bosses in jail, would only ''sing'' to Falcone, a fellow Sicilian he regarded as an honorable man.

For Falcone's colleagues, no victory is safe. Andreotti, for instance, is lobbying for fewer guarantees of protection from prosecution for pentiti, a move that would likely discourage the Mafia defections Falcone worked so hard to win.

And prosecutors still have to battle age-old Sicilian thinking that loyalties belong to the family, not the law.

The mother of a young woman who had collaborated with Borsellino refused in shame to attend the funeral of the daughter, who committed suicide in despair after Borsellino's death. The mother later tore her daughter's photograph off the gravestone.

Falcone and his wife, Francesca Morvillo, a judge who worked with Palermo's juvenile delinquents, chose not to have children because of their dangerous life.

''You didn't want children 3/8'' said a torn, smudged sheet of paper left at the fig tree by Luisa, a schoolgirl from Naples.

''I would have wanted you as a daddy 3/8''