In most states in this country, the surviving next of kin has the final determination as to how the deceased's remains are ultimately taken care of in the event that other close family members cannot come to a uniform agreement taking into great consideration the deceased's final wishes.Meaning, if there is a writing signed by the person who passes stating a certain way for burial or a desire for cremation, those wishes are typically respected by family members and the closest surviving relative.Since your father had a girlfriend but he never divorced your mother, the girlfriend would have no say as to have your father's remains are disposed of.Good question.