29A-2-102. Share of the spouse.
The intestate share of a decedent's surviving spouse is:
(1) 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;
(2) The first $100,000, plus one-half of any balance of the intestate estate, if one or more of the decedent's surviving descendants are not descendants of the surviving spouse.

29A-2-103. Shares of heirs other than surviving spouse.
Any part of the intestate estate not passing to the decedent's surviving spouse under § 29A-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:

(1) To the decedent's descendants by representation;
(2) If there is no surviving descendant, to the decedent's parents equally if both survive, or to the surviving parent;
(3) If there is no surviving descendant or parent, to the descendants of the decedent's parents or either of them by representation;
(4) 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 by representation to the descendants of the decedent's paternal grandparents or either of them if both are deceased; 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.

29A-2-105. No taker.
If there is no taker under the provisions of this chapter, the intestate estate passes to the State of South Dakota as provided in § 29A-3-914.

29A-2-106. Representation.
(a) If, under § 29A-2-103 (1), a decedent's intestate share or a part thereof passes "by representation" to the decedent's descendants, the estate or part thereof is divided into as many equal shares as there are (i) surviving children of the decedent, if any, and (ii) children of the decedent who failed to survive the decedent but who left descendants who survive the decedent. Each surviving child is allocated one share. The share of each child who failed to survive the decedent but who left descendants who survive the decedent is divided in the same manner, with subdivision repeating at each succeeding generation until the share is fully allocated among surviving descendants.

(b) If, under section § 29A-2-103 (3) or (4), a decedent's intestate estate or a part thereof passes "by representation" to the descendants of the decedent's parents or either of them or to the descendants of the decedent's paternal or maternal grandparents or either of them, the estate or part thereof is divided into as many equal shares as there are (i) children of the designated ancestor or ancestors who survived the decedent, if any, and (ii) children of the designated ancestor or ancestors who failed to survive the decedent but who left descendants who survive the decedent. Each surviving child is allocated one share. The share of each child who failed to survive the decedent but who left descendants who survive the decedent is divided in the same manner, with subdivision repeating at each succeeding generation until the share is fully allocated among surviving descendants.

29A-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.