Family and Kin

For China the starting point is the work of Maurice Freedman:
CALL NO.     HQ667 .F68 1971.
AUTHOR       Freedman, Maurice.
TITLE        Chinese lineage and society; Fukien and Kwangtung.
IMPRINT      London, Athlone Press; New York, Humanities Press, 1971.

CALL NO.     HQ667 .F3.
TITLE        Family and kinship in Chinese society. Contributors: Ai-li S. 
               Chin [and others] Edited by Maurice Freedman.
IMPRINT      Stanford, Calif., Stanford University Press, 1970.

CALL NO.     HQ667 .F68 1970.
AUTHOR       Freedman, Maurice.
TITLE        Lineage organization in southeastern China.
IMPRINT      London, University of London, Athlone Press; New York, Humanities
               Press Inc. [1970]

CALL NO.     HN733 .F73.
AUTHOR       Freedman, Maurice.
TITLE        The study of Chinese society : essays / by Maurice Freedman ; 
               selected and introduced by G. William Skinner.
IMPRINT      Stanford, Calif. : Stanford University Press, 1979.
To get a sense of what this is all about, consider this fragment from G. William Skinner's introduction to The Study of Chinese Society:
...the debate over the idea that the Chinese family was an enduring corporation. Freedman argued that it was not. As he put it in Essay 17, "the Chinese family is a property-owning estate whcih dissolves on the death of each senior generation to reform into successor-estates, none of which can be said to have the identity inhering in its predecessors. As each son is born (or adopted) he is automatically endowed with a potential share in the family estate." yes and no, replied Arthur Wolf [1974], pointing out that Freedman has reference here to the descent-group aspect of the family at the expense of its residence-group aspect. In Wolf's view, the Chinese family is an amalgam of two distinct institutions: the chia, the basic unit of production and consumption and a component part of the empire, and the line, property-owning descent group and the social unit responsible for domestic ancestral rites. Sons are born to chia, not to lines; but they are recruited to lines either through recognition by the line's head or by adoption. And both lines and families dissolve on division. Freedman admired this bold reformulation, but died before he could respond in print... (pg. iii)

Here's another:

In moving from the family to the lineage, we encounter another of Freedman's dualisms --that between the cult of immediate jural superiors and the cult of descent groups. The former, the care and commemoration of forebears "as it were for their own sake." is a domestic cult associated with the family (or as Arthur Wolf would have it, the line), whereas the latter, "a set of rites linking together all the agnatic descendants of a given forebear", is associated with extrafamilial kin groups: clans, lineages, and lineage segments. Little was achieved in the study of Chinese ancestor worship until this distinction was clearly drawn by Freedman... (pg. xix)

Freedman's The Family in China, Past and Present (from Pacific Affairs, 1961, available via JSTOR) summarizes eloquently.