As someone who is personally a minarchist, I'm wondering how the Non-Aggression Principle would be enforced in the AnCap model.
Given that there definitely is definitely no executive branch, people would obviously have to take personal defence into their own hands. But would there be trials for people who pollute your land? Surely not all 'aggression' is the type that would give you the right to shoot someone on the spot?
On another note, what about defense from external forces? You would need an organised and unified military. While I hate the government, I cannot understand the AnCap solution to an armed conflict with another country .
Let's say a person breaks a contract with their apartment. Well only enough force is allowed to forcibly remove the person of he won't leave voluntarily once it's clear he has no more right there. I Don't have all the answers. I'm not a legal theorist but I'm trying with this.
That sounds quite reasonable. But what about situations where the lines are a little blurry and both parties disagree? We would need a court to decide the outcome and punishment. There should definitely be a judicial branch of government for sure. I know it's a work in progress.