A. Property may be divided in kind without the necessity of drawing lots therefor when all of the co-owners who are competent agree to the proposed partition, and the court has authorized it on behalf of the incompetent co-owner, as provided in Articles 4271 and 4566.
B. In such event there is no necessity for a judicial partition, and the division of the property may be made by agreement of the co-owners, with the legal representative of an incompetent co-owner executing the act of partition in behalf of the incompetent whom he represents.