Whoa. I've never heard of this culture. As a woman, I think this would be awesome. Since it makes such good genetic sense, why aren't there more cultures like this? The women of this matrilineal society shun marriage and raise their kids in homes with their entire extended families—but no dads. By most accounts, children seem to do just fine under the arrangement. "They are a society that we know hasn't had marriage for a thousand years, and they've been able to raise kids successfully," said Stephanie Coontz, family studies professor at the Evergreen State College in Olympia, Washington. Men of the Mosuo, who live around Lugu Lake on the border between Yunnan and Sichuan Provinces, do help to raise kids—just not their own, with whom the men typically have only limited relationships. Instead the men help look after all the children born to their own sisters, aunts, and other women of the family. Rather than "one father with a kid, it will be four or five uncles. That [father] role is shared among a number of people, and these are very large extended families," explained John Lombard, director of the Lugu Lake Mosuo Cultural Development Association. The unusual parenting arrangement makes genetic sense, in terms of extending the family line—and many Mosuo men actually think of it that way, Lombard said. "If you [father] a child with another woman, you can never be absolutely sure that the child really shares your genes," he said. "But if your sister has a child, you can be 100 percent sure that the kid shares some of your genes."...
are they currently this way as well? No marriages, no husbands, property being passed down through daughters?
No idea, really. They are from Kerala and the one I knew was born in Mumbai and did not follow it exactly http://en.wikipedia.org/wiki/Marumakkathayam
The catch is that women have to own or control wealth to make it work (they have to be able to coerce, if necessary, their male relatives' contribution) - and the uncertainty of genetic relationship that it covers can be handled in other ways, once men control the wealth (severe punishments for female straying or unchastity, etc). Something like that seems to have been normal among the northern British Isles folk (my own ancestors), which was ended by force when the English conquered them, and I recall having run into several accounts of different tribal people (Pacific Islands, Southern Asia, Africa, don't recall any from the Americas) in which by custom uncles rather than fathers raised children - a central feature.
Don't get too excited about matrilineal systems; they are not the same thing as matriarchal systems. In many instances, matrilineal systems are actually strongly patriarchal, with the whole female inheritance thing being an artifact of odd circumstances. For example, island cultures on prominent trade routes, where the men all work in shipping and sailing and so are away most of the year, such as Lakshadeep.
The Pictish kingship was passed down through the female line, because at least you knew who the mother was... http://hejira.com/cp_lecture_5.html
quadraphonics, the Mosuo, are actually a matriarchy. If no suitable woman can take over a house, an outside woman may become "adopted" and made de facto head of the family. The major decisions (financial or otherwise) are taken by the women, or men are charged by the women with taking the decisions (e.g. if it is in their field of expertise). The women also decide if and which man (from other families, of course) they bed. While couples may form, the man remains attached to his family (and the woman to hers). More interestingly, the woman is allowed to switch man as she likes and does not need to fear social repression due to it. In fact, the men are supposed to come over after dawn and leave the next morning, so that it really remains a kind of very private thing. Point is, however that the male has to be invited and furthermore, have right over their children. Those all remain with the woman and her family.