A set S of vertices in a connected graph G is an irregular dominating set if the vertices of S can be labeled with distinct positive integers in such a way that for every vertex v of G, there is a vertex u 2 S such that the distance from u to v is the label assigned to u. If for every vertex u 2 S, there is a vertex v of G such that u is the only vertex of S whose distance to v is the label of u, then S is a minimal irregular dominating set. A graph H is an irregular domination graph if there exists a graph G with a minimal irregular dominating set S such that H is isomorphic to the subgraph G[S] of G induced by S. In this paper, all irregular domination trees and forests are characterized. All disconnected irregular domination graphs are determined as well.