Tommaso Gagliano is born 29 May 1883 in Corleone and baptized Thomam the next day, named after his paternal grandfather. His parents are Luciano Gagliano and Lucia Oliveri. His godfather is the unmarried Michaele Provenzano.
Open Issue: According to the Italian language Wikipedia page on the mafia in Corleone, Tommaso's father is Angelo Gagliano, who is a former capo in the mafia in Corleone. However, Angelo does not marry until 1902, while the same source gives Tommaso's birth year as 1883.
Tommaso and his sister, Luigia, stand as godparents in 1899.
A margin note on his baptismal record says that Tommaso marries in New York at the Church of S. Lucia on 23 October 1921 to Giuseppa Pomilla, daughter of Biagio Pomilla and Serafina Milone, who was also born in Corleone.
In 1925, the New York state census taken 1 June finds Thomas Gagliano, Josephine Gagliano, Angelina Pomilla (“Pommilla”), Millie Pomilla, and Nunzio Pomilla in sequence, living on E 227th St in Bronx County in Block 13, ED 42, AD 6, Ward X of New York City. They are the last names in the enumeration of Block 13. All were born in Italy. Thomas is a building contractor. Angelina is a sketcher. Millie is a machine operator. Nunzio is a building contractor. Thomas, 41 (b. 1884), and his wife, Josephine, 34 (b. 1891), were naturalized 23 June 1915. Living with him are his siblings in law, Angelina, 31 (b. 1894), Millie, 30 (b. 1895), and Nunzio, 30 (b. 1895). (Nunzio is a twin of Carmela, must be Millie.) Only Nunzio has been naturalized, also in 1917. The month is not legible but the day is the 29th.
Tommaso is an important financier of the Castellammarese War, through his United Lathing Company. Giuseppe Morello is an original investor. According to Valachi, Gagliano supplied most of the funds for Maranzano's struggle against Masseria. The estimate of Gagliano's support is $140-150K (more than $2M in 2017 dollars), a number Critchley considers inflated.
According to the Wikipedia article, Tommy Gagliano is boss of the Lucchese crime family, one of the "Five Families" of New York, around 1930.
Gagliano's only jail sentence, in May 1932, is for income tax evasion related to his lathing company. 
According to Selwyn Raab's account, Tommy Lucchese is the long-time lieutenant to Tommy Gagliano in the Bronx. When Gagliano becomes fatally ill with a heart condition in the early 1930s, he hands the family business to Lucchese. The organization is subsequently known as the Lucchese crime family. Gagliano does not die in the next few years, and by Lucchese's account, not until 1951.
These names appear on a list of US citizens on the SS Rex sailing from Naples on 12 April 1939 and arriving in New York on 20 April:
Tommaso Gagliano, 53 (b. 1886), Giuseppa Gagliano, 47 (b. 1882), both married, are in lines 5 and 6. Line 7 is crossed out, Giuseppe di Carlo, 53 (b. 1886), indicating he did not travel. His address looks like 2333 80th St, Brooklyn. Ignazio Milone, 40 (b. 1899), single, is in line 8.
Tommaso and Giuseppa are at 638 E 227th St, New York, and Ignazio is at 709 E 226th St, NY. Both addresses are in the Bronx, about two blocks from one another. Ignazio was naturalized 26 Sep 1929. Tommaso was naturalized on 23 June 1925. Giuseppa Gagliano was naturalized by marriage, no date given.
The actual date of Gagliano's death is still uncertain. In 1951, Gaetano "Tommy" Lucchese stated during the Senate hearings on organized crime that Gagliano died on 16 February 1951.
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