  We prove that a simple distributed algorithm finds a constant approximation
of an optimal distance-$k$ dominating set in graphs with no $K_{2,t}$-minor.
The algorithm runs in a constant number of rounds. We further show how this
procedure can be used to give a distributed algorithm which given $\epsilon>0$
and $k,t\in \mathbb{Z}^+$ finds in a graph $G=(V,E)$ with no $K_{2,t}$-minor a
distance-$k$ dominating set of size at most $(1+\epsilon)$ of the optimum. The
algorithm runs in $O(\log^*{|V|})$ rounds in the Local model. In particular,
both algorithms work in outerplanar graphs.
