What was the Mormon to Utah?
The headquarters of the Church of Jesus Christ of Latter-day Saints (commonly called the "Mormon" church) is in Salt Lake City, Utah. It has been located there since 1847, when a large group of Mormons traveled there seeking religious freedom. Today, about 1/10 (1.8 million out of 13.8 million) of the total Mormon Church membership lives in Utah.
The Mormon Trail was traveled by Mormon Pioneers from Illinois to Utah after they had been kicked out of Illinois. It was then traveled by Mormon converts from Europe and Canada as they immigrated to "Zion" (the Mormon settlements in Utah). The trail was mostly discontinued after the railroad reached Salt Lake City.
No. The Church of Jesus Christ of Latter-day Saints (the "Mormon" church) does not run the state of Utah. The Government of the State of Utah runs the state of Utah. Theocratic governments are not allowed within the United States. About 60-70% of the state-level politicians in Utah are members of the Mormon church, which is simply a reflection of the fact that about 65% of the residents of Utah are practicing Mormons.