My question is about the probability distribution over the possible size of the containing cluster of a randomly chosen node in an Erdős–Rényi random graph.

Let G(n,p) be an Erdős–Rényi random graph (with n nodes, and each edge included with probability p). Uniform-randomly select one of the n nodes from the graph. What is the probability of the node belonging to a cluster of size k, for k in {1,2,..,n}?