If the estate is still in probate and you are not on the utility accounts, the estate (i.e. the money and assets left behind by your mother) is responsible for paying these bills, and the executor (if there was a will) or court-appointed administrator or personal representative (if there is no will) should be paying these out of estate assets. Note that the estate, through its executor, etc. could hold you responsible for the bills if you are living there and therefore causing them: i.e. the estate could in theory sue you for the costs you are causing it, but if you are the sole beneficiary, this is clearly not going to happen.If you put any accounts in your name, you are responsible: in that case, you contractually took on the obligation to pay them.If the utilities are not paid, regardless of who should pay them, they could be shut off, of course.