I agree with funkyanarchy. I also agree with the second paragraph. Relocation would be the most normal response in an anarchic world as it was in history and is in the present. That is what people do. But now there are too many people and if anyone leaves to somewhere else, somewhere else is where other people also live.
Mass society anarchies by definition don't have any territories nor groups that dominate a territory's violence. This can mean a non-interventionist society or an ultra interventionist society would be an anarchic society. Given the mass, I would suspect ultra intervention would be the rule of the day, but in actual practice, the monopoly of violence would probably be seized by the delegate bodies of the institutions needed to exist in order to keep mass society from collapsing.
In a previous answer we talked about how the most simplistic definition of the state is also perhaps the most correct one. Monopoly on violence in a territory is all that is needed. Any formal or informal group can become this. The state is not necessarily the government. For post Revolutionary War in America, the state was *not* in the hands of the government, but rather in the hands of the powerful landowners. In Egypt today, the power of the state is not in the government, but in the military. In England it is the monarch and not the government. So whatever institutions exist in an anarchist society would control how violence is used in society, despite the lack of government and business apparatuses.
In a anarchist world without a massive population, typically those that hold similar values can leave an area where they may disagree with the people there. Opting to stay would mean there must be a way to resolve differences and forcing others out can lead to violence. This is less about guessing what would happen and more about how people behave without government intervention. I can't say this stuff wouldn't happen and just because there was an outbreak of violence doesn't mean a state just formed.