What would happen to the house if something happened to the owner?

We have a house its under our mom's name and we 4 brothers none of our names are on the house except her. If something were to happen to my mom would the house automatically be transferred to her kids which is us 4 brothers or would the state of Texas take it up? Also we know its safer to have our 4 names on it... show more We have a house its under our mom's name and we 4 brothers none of our names are on the house except her. If something were to happen to my mom would the house automatically be transferred to her kids which is us 4 brothers or would the state of Texas take it up? Also we know its safer to have our 4 names on it as well since we are her kids how much does it cost to have our names on the house or the will? Is a lawyer the right person to ask or the state of texas or who? Thanks!!!!
Update: The house is paid off there never was a mortgage or bank parents bought it and paid for it in full.
Update 2: Also if anything happens to our mom we do not want to sell the house or anything we all want to still live in it we just want to make sure the house doesnt go to the states of texas or the city we live in thats all.
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