New results have recently been added to the Law Surname DNA project. The project was started in 2007 and now has 50 members. To date, we've identified two lineages (and perhaps two more) that each share a common ancestor. The balance of the members are "unassigned", which is to say that they don't have any matches yet. This isn't surprising as the Law/Laws surname originated at various locations in Scotland, Ireland and England. We expect additional matches as our membership grows. Details can be found at: www.worldfamilies.net/surnames/l/law/
DNA testing is useful for surname studies because one type of DNA (Y-DNA), just like the family name, is passed down directly from father to son. Thus, women can't test their Y-DNA, but they can have their fathers or brothers get tested. If two men share the same surname and their DNA matches closely, they are likely to have a common ancestor within a recent time frame.
I encourage you to join if you match any of the surnames in the project. Please let me know if you have any questions. Regards, Kirby Law