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World communism, also known as international communism or global communism, is the terminal stage of development of the (future) history of communism in Marxist theory. It has also been equated to the Comintern (Communist International). This is the meaning that typically and historically has been meant by opponents of communism. World communism is closely related and connected to stateless communism.
Marxist theory may treat world communism as utopian, but it is the transition to world communism that attracts attention. World communism is to be achieved by world revolution, according to a theory that was popular in the period 1917 to around 1933 (at least). World communism is incompatible with the existence of nation-states, so according to an older theory there will be an abolition of the state preceding world communism.
Abolition of the state is not incompatible with world revolution, but is not in itself a distinctively Marxist doctrine. It was held by various socialist and anarchist thinkers of the nineteenth century. An apparent alternative is a theory going back to Karl Marx, speaking of the "withering away of the state".
The crux here is a text of the Friedrich Engels, from his Anti-Dühring. It is often cited as "The state is not 'abolished,' it withers away.” This is from the pioneer work of historical materialism, a formulation of Marx's idea of a materialist conception of history. The withering away of the state is a graphic formulation, that has passed into cliché. The translation (Engels was writing in German) is also given as: "The state is not 'abolished'. It dies out." Reference to the whole passage shows that this happens only after the proletariat has seized the means of production. There has been a revolution.
The schematic is therefore revolution, transitional period, utopian period.
For Lenin the transitional period, which for Engels was reduced to a single act, has become extended and "obviously lengthy". In the same place he argues strongly that Marx's conception of communist society is not utopian, but takes into account the heritage of what came before.
This gives, at least roughly, the position on world communism as the Comintern was set up in 1919: world revolution is necessary for the setting up of world communism, but not immediately or clearly sufficient.