There are no such thing as "Squatter's Rights" in any state of the United States including Utah. Squatter's rights are legal in Europe -- particularly England -- where a person can move into a property and take it over and remain in it for a short period of time to declare ownership (usually about a year or so). Those laws were not adopted in the US when we modeled our legal system after the English system. The closest thing that we have to Squatter's Rights are the laws of Adverse Possession -- Utah Code 72B-2-208 - which states that the legal owner of a property has rights to it over anyone else unless someone holds the property adversely for 7 years. To hold a property in adverse possession means that you must move in and take it over without permission from the owner for a continuous period of 7 years without the owner noticing or doing anything about it for that full 7 year period -- typically adverse possession is claimed on pieces of land or open land that a person might take over (such as one neighbor putting a fence over 20 feet of the other neighbor's property and if the other neighbor never does anything about the fence and 7 years pass the neighbor who put the fence up and took the land can then claim that the possession of the 20 feet of the land was open and in plain view of the owner and the owner never did anything about it, so the neighbor who took the 20 feet can claim full ownership of that 20 feet of land). Here is the utah statute: http://le.utah.gov/~code/TITLE78B/htm/78B02_020800.htm
In a case with a house as you describe, you would have to move in and openly stay there with the knowledge of the owner of the house (who makes no move to eject you) for a full period of 7 years -- the problem with trying that is that the police can eject you if you cannot show legal ownership and you can be arrested for trespassing if you refuse to leave the property, so in the US you simply do not see people taking over abandoned houses because there is no legal way to do it for the length of time that it must be done in order to establish legal ownership of the property. You can read more about this by doing a search for Adverse Possession Utah.
I hope that helps. Good Luck.
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