After a person's death, the transfer of his or her property, or rights, to another person by virtue of their blood relationship or some other tie, is called inheritance.
The living relative is called the "warith" (heir), the deceased is called the "muruth" (one who bequeaths), and the right is called "irth" (inheritance). The relationship between a person born of another, or that of two persons who are born of a third, is called a blood relationship (nasab).
If the right of an heir is fixed in the Qur'an, he or she shall be counted in the category of those who receive inheritance as a matter of obligation, otherwise he or she shall be entitled to receive inheritance by virtue of blood relationship.
In the Holy Qur'an, the chief shares are six. The description of the shares and the inheritors is as follows:
1. The half-share (nisf):
a) the husband, provided that the wife has no son.
b) one daughter; here too the absence of a son is a condition.
c) a sister; here also the same condition applies
2. The quarter-share (rub'):
a) the husband, when the deceased wife's son inherits.
b) the wife, provided that the husband does not leave behind a son.
3. The eighth share (thamin): the wife, when the husband leaves a son.
4. The third-share (thulth). the mother, when there is no son; also some inheritors from the mother's side.
5. The two-thirds share: two daughters when there is no son.
6. The sixth-share (sudus): each of the father and the mother in the presence of a son; also an inheritor from the mother's side whether man or woman.
Those who are not included in the above settlements shall be inheritors on account of their blood relationship with the deceased, observing the rule that the share of the man is double that of the woman.
The heirs who are in a state of blood relationship with the deceased are divided into three groups:
(i) the mother, the father, sons, daughters (or failing these, their descendants).
(ii) grandfathers, grandmothers, brothers and sisters (or failing this, their descendants)
(iii) paternal uncles and aunts, maternal uncles and aunts (or failing this, their descendants)
The universal principle is that the presence of members of group (i) prevents members of group (ii) presents members of group (iii) inheriting. Thus, the one closer in blood-relationship acts as a barrier to the remoter, and this principle also holds within each group.
The only really significant difference between the Shi'ah and Sunni schools of jurisprudence in the laws of inheritance concerns the principles of " "awl" and "ta'sib" 3. The Imamiyah jurisprudents have proved by means of ahadith from the Ahlu'l-bayt (a.s.) that there is no 'awl or ta'isb in the matter of inheritance. This was also the opinion held by the great companions of the Holy Prophet. The well-known statement of Ibn 'Abbas in which he speaks against 'awl and ta'sib can be taken as authoritative. There are also other grounds of proof for negating these two principles.
source : http://www.islamicecenter.com/e-library/logic_islamic_rules/logic_islamic_rules_makarem_subhani_03.html