We study the problem of random-assisted simulation of discrete broadcast channel in one-shot and i.i.d. setups. We derive one-shot inner and outer bounds of the set of attainable message-size pairs for simulating W YZ|X within some total variation distance (TVD) tolerance of ϵ. The inner bounds are based on the bipartite convex split lemma. Whereas the outer bounds are based on the properties of the multi-partite max information. Using these bounds, we establish a single-letter expression of the simulation region of a broadcast channel.