(a) Upon the death of the husband or the wife, 1/2 of the community property shall continue to belong to the surviving spouse and the other 1/2 shall pass in accordance with testamentary disposition by the deceased spouse, or, in the absence of testamentary disposition, then to the heirs at law and distributees of the deceased spouse in the manner provided by law, subject to the following provisions of this section.

  (b) The executor of the will or the administrator of the estate of the deceased spouse shall administer all of the community property which stands in the name of the deceased spouse, including the interests therein of the surviving spouse and of the deceased spouse, as well as the separate property of the deceased spouse. Such executor or administrator shall have the same rights, powers, and duties with respect to the administration and disposition of such community property, real and personal, as with respect to the separate property of the deceased spouse. All of the provisions of Act No. 288 of the Public Acts of 1939, as amended, with respect to the administration and disposition of property, real and personal, included in estates, shall be applicable with respect to such community property as well as with respect to such separate property. The probate court having jurisdiction of the estate of the deceased spouse shall determine whether and to what extent property being so administered constitutes separate property of the deceased spouse or community property and shall also determine whether and to what extent property standing in the name of the surviving spouse, or standing in the names of both the surviving spouse and the deceased spouse in such manner that by law, but for the provisions of this act, the surviving spouse would succeed thereto by reason of survivorship, constitutes separate property of the survivor or community property. Such determination shall be made upon application of the executor or administrator, the surviving spouse, or any other interested person, after such notice to the surviving spouse and any other interested person as the court may direct, and, in addition thereto, in any case where creditors of the estate have not yet been determined, notice shall be given as provided for in Act No. 288 of the Public Acts of 1939, as amended. Upon the making of such determination, the court shall enter an order in accordance therewith, including such directions to the executor or administrator and to the surviving spouse as to the execution and delivery of any conveyances, transfers, waivers, or releases as shall be appropriate to carry out the terms thereof, so that all property which constitutes community property shall be subject to administration by the executor or administrator and that which constitutes separate property of the surviving spouse shall be free from such administration, and all of the provisions of Act No. 288 of the Public Acts of 1939, as amended, which are applicable with respect to community property standing in the name of the deceased spouse, as hereinbefore provided, shall likewise be applicable with respect to all community property so subjected to administration by such executor or administrator.

  (c) In the order for and at the time of the determination of claims, such court shall also determine whether and to what extent claims and administration expenses are payable out of community property or out of separate property of the deceased spouse and those payable out of community property shall be charged equally against the half of the community property which belongs to the survivor and the half which passes in accordance with testamentary disposition of or to the heirs and distributees of the deceased spouse. No estate, inheritance, succession, or similar taxes payable by reason of the transfer upon the death of the deceased spouse of the interest of such spouse in community property shall be charged against the half of the community property which belongs to the surviving spouse.

  (d) When all claims and administration expenses for which the community property is liable have been fully satisfied, or appropriate provision has been made for their satisfaction, the court shall enter an order directing the executor or administrator to execute and deliver such instruments as shall be appropriate to transfer and convey 1/2 of the remainder of the community property to the surviving spouse and thereafter the interest of the surviving spouse in such property shall be that of a tenant in common. The probate court shall have authority to conduct any further hearing and to make any further determination which shall be incidental or necessary to carrying out the provisions of this act.

  (e) Notwithstanding any other provision of this act, any other person may rely, and shall be fully protected in so doing, upon the right of the surviving spouse to receive, manage, control, dispose of, or otherwise deal with property standing in the name of the surviving spouse, or standing in the names of both the surviving spouse and the deceased spouse in such manner that by law, but for the provisions of this act, the surviving spouse would succeed thereto by reason of survivorship.