I believe there are a number of related threads ongoing at this moment in time so I will try and keep my questioning specific. In a free society, I envision numerous firms offering justice services. Presumably, resolving disputes between two members of the same justice service would be easy; there would be standard rules to adhere to, or at least a respected and accepted arbitrator of problems. However, how are problems resolved when members of two different justice services come into dispute? How are situations between a member of a justice system and someone who is not a member of a justice system resolved? Is there are case where victims are merely dictating terms to transgressors?
How is the issue of the criminality/non-criminality of an act decided?
I guess, you could have agreements / contracts between the different agencies. Incidentally, this could lead to some form of private federalism, which is the way Nozick passes from anarchism to minarchism -
Or you could have a third party nominated as an arbitror in the insurance / security initial contract.
There was a story a few months earlier about the sheiks of Anbar province in Iraq, who have lately replaced the state courts as the providers of justice. The journalist described the process. Two conflicting parties came to the sheik looking for a resolution to their conflict. Before giving out his ruling, the sheik made them swear to abide by it. Once he had ruled both left a little bit disappointed, but nevertheless the conflict had been resolved.
To generalize and answer your question, everyone looking for justice is a member of the same system. Once the two conflicting parties agree that there is no reason to fight and instead to ask a judge for a solution, they have created their own justice system.