Myself in reply to the question of who would run the prisons:There would be not forced imprisonment, however the system would have to be set up in such a way that anyone giving aide and confort to a person known to be a criminal, would be held as a liable party the next time that person commited a crime. In this way, prepared food, hotels, and even clean water would be denied to a person who refused to isolate himself to the degree neccessary needed to protect society and to repay his victims. A criminal not agreeing to these program would be reduced the the level of an animal, scavengin for basic food, water and shelter, without any contort, save what he can provide for himself.
There would even be competition amoung these facilities to insure humane treatment and most economical allocation of resources, however there would alse be the counter force that these facilities would have to accept liability that thier inmates might cause to the community at large. The facilities would have the right to later demand repiration from the criminal, though the most violent would be the least likely to be able to pay in thier lifetime, and the most kept away from society, while the simple burglar could have enough time to work off any relapse that he might have.Even between "prisons" and "prisoners" there would still be the two way and voluntary negotiations that are the core of anarchic society.
I thought it brought out a even better side of anarchy than what stef was talking about in practical anarchy. Those who have been ostracized and have a debt for reparations are looking for a service. Someone to give them a job, and food and shelter, but to do so the prison would have to assume liability for thier actions in order for society at large to be properly reassured of thier saftey. (Pehaps even agreeing to double penalites for those already in the "prison" system. There is not reason that a individual should be forced to use any particular DRO's or arbitors prison of choice. Instead it should be a two way negotiation, balancing the prisonors interests, the prison's. To balance out extreme to prisons encourageing laziness, to owed reparations may stipulate through the trial a certain amount of funds needed to go to reperations per year.