Unless I missed it, there has been nothing written about how good Deadwood is at dramatizing the interplay between the state and capital. I reckon this happens at two levels of narrative that might be said to dramatize the international, interstate and internal relation between state and capital.
The background includes that which is said (all that Yankton business and the political horseplay of incorporating Deadwood into the USA) and what is not said (how the value of the colour on the world market leads to this dynamic of incorporation. Here in addition to Deadwood providing a political marxist history of American capitalism, it might also serve as a model of the Monroe Doctrine.)
The foreground consists in a narrative that might be said to include two periodisations of the interplay between the state and capital. The first consists in the foundation of state institutions to protect the interests of the ruling parties in Deadwood proper. (Here the ongoing gag that Farnum is the titular mayor also has its critical content.) The second consists in the clash between the institutions of this city-state as representative of localized capital and the figure of Hearst as a more powerful form of capital accustomed with the state doing his bidding. (From this perspective one can read the outrage Hearst experiences after being manhandled by Bullock as outrage that the state has not done his bidding.)
The figure of Bullock, as a violent psychopath who occasionally spouts democratic platitudes might also been seen as the ambivalent figure of the state personifying both its role as the force of value and its political ideals. As the force of value he serves to reinforce the process of primitive accumulation and subsumption that unfolds over the three seasons of Deadwood. But his fits of psychotic violence serve the interests of different capitalists who attempt to utilize him for their respective ends. At the same time his platitudes serve as the foundation for the egalitarianism of the public sphere that figures like Merrick buy into and which might be said to be represented in Bullock’s mediation between Steve and Hostetler.