The partition would be governed by the provisions of the Hindu Succession. Her successors are the children and her husband, if alive. In respect of the deceased children, their share in the joint property has devolved upon respective legal heirs.
In the given context, provisions of Sections 14, 15 and 16 are applicable -
Section 14. Property of a female Hindu to be her absolute property
(1) Any property possessed by a female Hindu, whether acquired before or after the commencement of this Act, shall be held by her as full owner thereof and not as a limited owner.
Explanation.-- In this sub-section, "property" includes both movable and immovable property acquired by a female Hindu by inheritance or devise, or at a partition, or in lieu of maintenance or arrears of maintenance, or by gift from any person, whether a relative or not, before, at or after her marriage, or by her own skill or exertion, or by purchase or by prescripttion, or in any other manner whatsoever, and also any such property held by her as stridhana immediately before the commencement of this Act.
(2) Nothing contained in sub-section (1) shall apply to any property acquired by way of gift or under a will or any other instrument or under a decree or order of a civil court or under an award where the terms of the gift, will or other instrument or the decree, order or award prescribe a restricted estate in such property.
Section 15. General rules of succession in the case of female Hindus.
(1) The property of a female Hindu dying intestate shall devolve according to the rules set out in section 16,
(a) firstly, upon the sons and daughters (including the children of any pre-deceased son or daughter) and the husband;
(b) secondly, upon the heirs of the husband;
(c) thirdly, upon the mother and father;
(d) fourthly, upon the heirs of the father; and
(e) lastly, upon the heirs of the mother.
(2) Notwithstanding anything contained in sub-section (1),
(a) any property inherited by a female Hindu from her father or mother shall devolve, in the absence of any son or daughter of the deceased (including the children of any pre-deceased son or daughter) not upon the other heirs referred in sub-section (1) in the order specified therein, but upon the heirs of the father; and
(b) any property inherited by a female Hindu from her husband or from her father-in-law shall devolve, in the absence of any son or daughter of the deceased (including the children of any pre-deceased son or daughter) not upon the other heirs referred to in sub-section (1) in the order specified therein, but upon the heirs of the husband.
STATE AMENDMENT
Kerala.--
Amendment of section 15.--In the Hindu Succession Act, 1956 (Central Act 30 of 1956), in section 15, after clause (b) of sub-section (2), the following clause shall be inserted, namely:--
"(c)" any property inherited by a female Hindu from her pre-deceased son shall devolve, not upon the other heirs referred to in sub-section (1) in the order specified therein, but upon the heirs of the predeceased son from whom she inherited the property."
[vide Kerala Act 17 of 2016, sec. 2].
Section 16. Order of succession and manner of distribution among heirs of a female Hindu.
The order of succession among the heirs referred to in section 15 shall be, and the distribution of the intestate's property among those heirs shall take place according to the following rules, namely:―
Rule 1.―Among the heirs specified in sub-section (1) of section 15, those in one entry shall be preferred to those in any succeeding entry, and those included in the same entry shall take simultaneously.
Rule 2.―If any son or daughter of the intestate had pre-deceased the intestate leaving his or her own children alive at the time of the intestates death, the children of such son or daughter shall take between them the share which such son or daughter would have taken if living at the intestates death.
Rule 3.―The devolution of the property of the intestate on the heirs referred to in clauses (b), (d) and (e) of sub-section (1) and in sub-section (2) of section 15 shall be in the same order and according to the same rules as would have applied if the property had been the father's or the mother's or the husband's as the case may be, and such person had died intestate in respect thereof immediately after the intestate's death.