Kürzlich, G\'{O}rska, Lema\'{N}czyk, and de la Rue characterized the class of
automorphisms disjoint from all ergodic automorphisms. Inspired by their work,
we provide several characterizations of systems that are disjoint from all
minimal systems.
For a topological dynamical system $(X,T)$, it is disjoint from all minimal
systems if and only if there exist minimal subsets $(M_i)_{i\in\mathbb{N}}$ von
$X$ whose union is dense in $X$ and each of them is disjoint from $X$ (we also
provide a measure-theoretical analogy of the result). For a semi-simple system
$(X,T)$, it is disjoint from all minimal systems if and only if there exists a
dense $G_{\Delta}$ set $\Omega$ in $X \times X$ such that for every pair
$(x_1,x_2) \in \Omega$, the subsystems $\overline{\mathcal{O}}(x_1,T)$ Und
$\overline{\mathcal{O}}(x_2,T)$ are disjoint. Furthermore, for a general system
a characterization similar to the ergodic case is obtained.

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