  Let $G$ be a countable discrete group. We give a necessary and sufficient
condition for a transitive $G$-system to be disjoint with all minimal
$G$-systems, which implies that if a transitive $G$-system is disjoint with all
minimal $G$-systems, then it is $\infty$-transitive, i.e. $(X^k,G)$ is
transitive for all $k\in\N$, and has dense minimal points. In addition, we show
that any $\infty$-transitive $G$-system with dense distal points are disjoint
with all minimal $G$-systems.
