> I have never heard any articulation of how the minimum can actually be zero that is anything other than a straw man.
I'm going to start out with the disclaimer that I am not personally opposed to all power relationships in the very broad sense used by some anarchists. I believe that there are universal natural rights, including both self-ownership and property, and that people have a right to enter into ongoing power relationships with others so long as they do so voluntarily of their own free will. So instead of "power relationships" the rest of this comment will use the term "force" or "aggression"—by which I mean power relationships involving violations of the individual's natural rights without their freely-given consent, except as a proportional defensive response to actual or imminent aggression by the other party. This is more-or-less the standard libertarian, anarcho-capitalist, or voluntaryist definition of aggression.
With all that said, the answer depends on whether you're talking about the minimum amount which is actually present or the minimum amount which can be considered "legitimate". It would be nice for both to be zero, of course, but I think we both agree that some amount of aggression is inevitable in practice—we aren't likely to eliminate all violent crime, for example, no matter how hard we try. The minimum amount of "legitimate" power, however, is trivial to simply define as zero. We are under no obligation to consider any act of aggression legitimate.
The distinction between anarchism and minarchism lies in how much aggression is deemed legitimate, not how much is present. The anarchist recognizes that aggression exists but does not consider any aggression to be legitimate, even when the goal is to reduce the overall level of aggression. The minarchist is willing to sanction a certain amount of aggression in order to achieve what they consider to be a greater good.
In my opinion the minarchist approach is neither principled nor pragmatic. It makes you an accessory to the aggression, normalizes it, and sets the stage for others to argue that ever increasing acts of aggression can be justified "for the greater good". Humans readily justify atrocities on the basis that a society organized "the right way" would somehow be free of violence or other ills. It doesn't work out well in practice. Better to aim for no aggression and consistently oppose such acts wherever you may find them rather than making exceptions.