The purist form of anarchy, with no 'rulers' at all, will never exist, because A, humans are social creatures; and B, there is strength in numbers.
Gangs would exist. Maybe family units like clans. Maybe fiefdom, with a rich employer leading employees. In some form, there will be small leadership.
There will be codes, guidelines, unspoken rules that cannot be broken. The criminals have a code; The rich employees have guidelines; the clans have unspoken rules. In some small form, there will be laws.
In that sense, anarchy is simply the lack of an overarching government, which provides a Big Leader and Constant Laws. An anarchic country will still have small leaders and theoretical laws. The groups of people, whether those groups are racial, familial, economic, regional, or religious groups, will be the ones who create and enforce their own laws and leaders. Those groups will be in constant conflict, because the job of a Big Leader and Constant Laws are to ensure peace, compromise, and justice. Without those concepts, might makes right and whoever is most charismatic or strongest or prettiest or Whatever is going to come out on top, at least for a little while.
Just some thoughts.