Your will should state , at death, they inherit the house. you would have that set up before hand, with any other instructions.
If you "gift" them the house, prior to death, their basis in the house is your basis. So, if you purchased it for $100k, that's their basis. But, if they "inherit" the home, their basis is the fair market value at the date of death. So, let's pretend the fair market value is $500k. If they sell if on that day for $500k, there would be no tax owed. If they sell it if it was a gift, then tax would be owed on $400 ($500 - $100).
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