If both parents be dead, then the portion which would have fallen to their share, by the above rules shall be disposed of in the same manner as if they had outlived the intestate and died in the possession and ownership of the portion thus falling to their share, and so on through ascending ancestors and their issue. [§3661.] [Sidenote: Wife and her heirs.] If heirs are not thus found, the portion uninherited shall go to the wife of the intestate, or to her heirs if dead, according to like rules; and if he has had more than one wife who either died or survived in lawful wedlock, it shall be equally divided between the one who is living and the heirs of those who are dead, or between the heirs of all, if all are dead, such heirs taking by right of representation. [§3662.] [Sidenote: Advancement.] Property given by an intestate by way of advancement to an heir, shall be considered part of the estate so far as regards the division and distribution thereof, and shall be taken by such heir, towards his share of the estate at what it would now be worth if in the condition in which it was given to him. But if such advancement exceeds the amount to which he would be entitled, he cannot be required to refund any portion thereof. [§3663.] A gift to an heir by way of advancement, cannot be considered as any part of the estate for the purpose of increasing the distributive share of the widow, but is to be estimated as part of such heir's share of the property, after the allowance to the wife of her interest. [Sidenote: Where there are no heirs.] If there be property remaining uninherited, it shall escheat to the state. [§3665.] [Sidenote: Illegitimate children. Inherit from mother.] Illegitimate children inherit from the mother and the mother from the children. [§3670.] A child born at any time during lawful wedlock is presumed by the law to be legitimate, but where questions of inheritance are involved, this presumption may be overcome by proof to the contrary. [Sidenote: Inherit from father.] They shall inherit from the father whenever the paternity is proven during the life of the father, or they have been recognized by him as his children, but such recognition must have been general and notorious or else in writing. [§3671.] The recognition in writing need not be a formal avowal. Any writing, as by letter or otherwise, is sufficient. For the purposes of inheritance an illegitimate child stands on exactly the same footing as if it were legitimate after it has been recognized by the father, and the birth and recognition of such child revoke a will in the same manner as the birth of a legitimate child, subsequent to the execution of the will. [Sidenote: Father inherits from child.] Under such circumstances, if the recognition of relationship has been mutual, the father may inherit from his illegitimate children. [§3672.] CHAPTER IX. HOMESTEAD AND EXEMPTIONS. [Sidenote: Homestead exempt.]