\begin{tikzpicture}
\umlbasicstate[name=state]{I am a state}
\umltrans[recursive=-20|20|4cm, name=assoc, recursive direction=right to right]{state}{state}
\draw (assoc-1) node[fill=black, circle, inner sep=0.1cm] {} node[below=0.2cm] {relname-1};
\draw (assoc-2) node[fill=black, circle, inner sep=0.1cm] {} node[right=0.2cm] {relname-2};
\draw (assoc-3) node[fill=black, circle, inner sep=0.1cm] {} node[right=0.2cm] {relname-3};
\draw (assoc-4) node[fill=black, circle, inner sep=0.1cm] {} node[right=0.2cm] {relname-4};
\draw (assoc-5) node[fill=black, circle, inner sep=0.1cm] {} node[above=0.2cm] {relname-5};
\end{tikzpicture}