75-2-102. Intestate share of spouse.
(1) The intestate share of a decedent's surviving spouse is: (a) the entire intestate estate if:
(i) no descendant of the decedent survives the decedent; or
(ii) all of the decedent's surviving descendants are also descendants of the surviving spouse;
(b) the first $50,000, plus 1/2 of any balance of the intestate estate, if one or more of the decedent's surviving descendants are not descendants of the surviving spouse.
(2) For purposes of Subsection (1)(b), if the intestate estate passes to both the decedent's surviving spouse and to other heirs, then any nonprobate transfer, as defined in Section 75-2-206, received by the surviving spouse is chargeable against the intestate share of the surviving spouse.

75-2-103. Share of heirs other than surviving spouse.
(1) Any part of the intestate estate not passing to the decedent's surviving spouse under Section 75-2-102, or the entire intestate estate if there is no surviving spouse, passes in the following order to the individuals designated below who survive the decedent:
(a) to the decedent's descendants per capita at each generation as defined in Subsection 75-2-106(2);
(b) if there is no surviving descendant, to the decedent's parents equally if both survive, or to the surviving parent;
(c) if there is no surviving descendant or parent, to the descendants of the decedent's parents or either of them per capita at each generation as defined in Subsection 75-2-106(3);
(d) if there is no surviving descendant, parent, or descendant of a parent, but the decedent is survived by one or more grandparents or descendants of grandparents, half of the estate passes to the decedent's paternal grandparents equally if both survive, or to the surviving paternal grandparent, or to the descendants of the decedent's paternal grandparents or either of them if both are deceased, the descendants taking per capita at each generation as defined in Subsection 75-2-106(3); and the other half passes to the decedent's maternal relatives in the same manner; but if there is no surviving grandparent or descendant of a grandparent on either the paternal or the maternal side, the entire estate passes to the decedent's relatives on the other side in the same manner as the half.
(2) For purposes of Subsections (a), (b), (c), and (d), any nonprobate transfer, as defined in Section 75-2-205, received by an heir is chargeable against the intestate share of such heir.
 

75-2-105. No taker.
If there is no taker under the provisions of this chapter, the intestate estate passes to the state for the benefit of the state school fund.

75-2-106. Definitions - Per capita at each generation
(2) (a) If, under Subsection 75-2-103(1)(a), a decedent's intestate estate or a part thereof passes "per capita at each generation" to the decedent's descendants, the estate or part thereof is divided into as many equal shares as there are:
(i) surviving descendants in the generation nearest to the decedent which contains one or more surviving descendants; and
(ii) deceased descendants in the same generation who left surviving descendants, if any. (b) Each surviving descendant in the nearest generation is allocated one share.
(c) The remaining shares, if any, are combined and then divided in the same manner among the surviving descendants of the deceased descendants as if the surviving descendants who were allocated a share and their surviving descendants had predeceased the decedent.
(3) (a) If, under Subsection 75-2-103(1)(c) or (d), a decedent's intestate estate or a part thereof passes "per capita at each generation" to the descendants of the decedent's deceased parents or either of them or to the descendants of the decedent's deceased paternal or maternal grandparents or either of them, the estate or part thereof is divided into as many equal shares as there are:
(i) surviving descendants in the generation nearest the deceased parents or either of them, or the deceased grandparents or either of them, that contains one or more surviving descendants; and (ii) deceased descendants in the same generation who left surviving descendants, if any. (b) Each surviving descendant in the nearest generation is allocated one share. (c) The remaining shares, if any, are combined and then divided in the same manner among the surviving descendants of the deceased descendants as if the surviving descendants who were allocated a share and their surviving descendants had predeceased the decedent.

75-2-107. Kindred of half blood.
Relatives of the half blood inherit the same share they would inherit if they were of the whole blood.