The state was the official representative of the whole of society, its concentration in a visible body, but it was so only in so far as it was the state of that class which in its time represented the whole of society: in antiquity, the state of the slave-owning citizens, in the Middle Ages of the feudal nobility, in our time, of the bourgeoisie. When ultimately it becomes the real representative of the whole of society, it renders itself superfluous. As soon as there is no social class to be held in subjection any longer, as soon as class domination and the struggle for individual existence based on the anarchy of production existing up to now are eliminated together with the collisions and excesses arising from them, there is nothing more to repress, nothing necessitating a special repressive force, a state. The first act in which the state really comes forward as the representative of the whole of society -- the taking possession of the means of production in the name of society -- is at the same time its last independent act as a state. The interference of the state power in social relations becomes superfluous in one sphere after another, and then dies away of itself. The government of persons is replaced by the administration of things and the direction of the processes of production. The state is not "abolished", it withers away. It is by this that one must evaluate the phrase "a free people's state" with respect both to its temporary agitational justification and to its ultimate scientific inadequacy, and it is by this that we must also evaluate the demand of the so-called anarchists that the state should be abolished overnight.

Engels, Socialism: Utopian and Scientific

The "Administration of Things" refers to a fully centralized, publicly owned economy, but without "special bodies of armed men" to enforce class distinctions. Marx's predictions for Communism came from analyzing the trajectory of Capitalism and predicting forward, not engineering an ideal society and working backwards.