If only my father's name is on the deed what happens to his house when he passes?

If your dad dies and does not have a Will, his assets will be divided up among his heirs equally.  With respect to the house, the executor of the estate will either convey it over to his children as they are the rightful owners in equal shares or the executor will sell the house and give each of the heirs the proceeds from the sale in equal shares.  I suggest that your dad convey the house to whoever he wants to have the property or draft a Will to make sure that his assets go to the people that he wants.  You can have a will drafted fairly quickly; however, you will need to make sure that you have a lawyer draft it; I do not suggest downloading a will form off the internet.