The way Donald J. Trump tells it, his first solo project as a real estate developer, the conversion of a faded railroad hotel on 42nd Street into the sleek, 30-story Grand Hyatt, was a triumph from the very beginning.

The hotel, Mr. Trump bragged in “Trump: The Art of the Deal,” his 1987 best seller, “was a hit from the first day. Gross operating profits now exceed $30 million a year.”

But that book, and numerous interviews over the years, make little mention of a crucial factor in getting the hotel built: an extraordinary 40-year tax break that has cost New York City $360 million to date in forgiven, or uncollected, taxes, with four years still to run, on a property that cost only $120 million to build in 1980.

The project set the pattern for Mr. Trump’s New York career: He used his father’s, and, later, his own, extensive political connections, and relied on a huge amount of assistance from the government and taxpayers in the form of tax breaks, grants and incentives to benefit the 15 buildings at the core of his Manhattan real estate empire.