Like the 'communes' of the Spanish civil war, the society that existed in the region occupied by the Makhnovchina is consistently upheld as the true heir of the October Revolution / the great revolutionary wave.
"Thirdly, and even more embarrassingly for the Leninists, numerous examples exist both from revolutionary Russia at the time and from earlier and later revolutions that suggest far from Bolshevik tactics being the most efficient way of defending the revolution other methods existed which looked to the massive creative energies of the working masses unleashed by the revolution.
During the Russian Revolution the biggest example of this is found in South-Eastern Ukraine. For much of the Civil War this area operated without a centralised state apparatus of the Bolshevik type and was, instead, based on the anarchist idea of Free Soviets. There "the insurgents raised the black flag of anarchism and set forth on the anti-authoritarian road of the free organisation of the workers." [Arshinov, The History of the Makhnovist Movement, p. 50] The space in which this happened was created by a partisan force that instead of using the "efficiency" of executions for desertion, tsarist officers appointed over the rank and file soldiers' wishes and saluting so loved by the Bolsheviks instead operated as a volunteer army with elected officers and voluntary discipline. This movement was the Makhnovists, named after its leader, the Ukrainian anarchist Nestor Makhno. The Black Flag which floated over the lead wagon of the Insurgent Army was inscribed with the slogans "Liberty or Death" and "The Land to the Peasants, the Factories to the Workers." These slogans summarised what the Makhnovist were fighting for -- a libertarian socialist society. At its height in the autumn of 1919, the Maknovists numbered around 40,000 and its extended area of influence corresponded to nearly one third of the Ukrainian Soviet Republic, comprising a population of over seven million.
It is this that explains the importance of the Makhnovists. As historian Christopher Reed notes, the "Bolsheviks' main claim to legitimacy rested on the argument that they were the only ones capable of preventing a similar disaster [counter-revolution] for the workers and peasants of Russia and that their harsh methods were necessary in the face of a ruthless and unrelenting enemy." However, Reed argues that "the Makhno movement in the Ukraine suggests that there was more than one way to fight against the counter-revolution." [From Tsar to Soviets, pp. 258-9] This is why the Makhnovist movement is so important, why it shows that there was, and is, an alternative to the ideas of Bolshevism. Here we have a mass movement operating in the same "exceptional circumstances" as the Bolsheviks which did not implement the same policies. Indeed, rather than suppress soviet, workplace and military democracy in favour of centralised, top-down party power and modify their political line to justify their implementation of party dictatorship, the Makhnovists did all they could to implement and encourage working-class self-government.
As such, it is difficult to blame the development of Bolshevik policies towards state-capitalist and party-dictatorship directions on the problems caused during the revolution when the Makhnovists, facing similar conditions, did all they could to protect working- class autonomy and freedom. Indeed, it could be argued that the problems facing the Makhnovists were greater in many ways." - Makhno FAQ
Is it accurate to say that 'no state' existed in revolutionary Ukraine? How were the workers and peasants organized?
I did a cursory search but didn't find much relating to the Ukraine under Makhno's army in the ICC's press back issues- it seems like an important topic, as there are several texts concerning the Spanish civil war and the 'communes'.