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I thought that just one state without any arrow coming out would do the job, but it looks like it's more complicated than that.

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Since $\emptyset^* = \{\varepsilon\}$, the NFA you are looking for simply has one state which is both the start state and the accept state.

Intuitively, you can also think of $\emptyset^*$ as "reading nothing $0$ or more times". Hence your start state should have loops that "read nothing", i.e. no loops!