There is no single answer to this. Society itself is experimental and iterative. Each nation's starting point for communism will be different, therefore administration of each communist experiment will be adapted to unique circumstances. Each nation's development path of communism will be different, therefore each nation's administration of that development will be different.
We do not yet know if all communist experiments will converge towards some shared administrative phenomena. There are plenty of people who have explored this in thought experiments, there are 6 communist experiments we can look to for real world lab results (China, USSR, Vietnam, Laos, DPRK, Cuba, am I forgetting one?), there are several other experiments we can look at (Paris Commune, Gotha Programme, Rojava, Zapatismo, others) but none of these could be considered the answer, just empirical evidence we can use to understand your question better and explore the set of possible answers, which is far larger than the experience we have so far.