  Following problems posed by Gy\'arf\'as, we show that for every
$r$-edge-colouring of $K_n$ there is a monochromatic triple star of order at
least $n/(r-1)$, improving a previous result by Ruszink\'o.
  An edge colouring of a graph is called a local $r$-colouring if every vertex
spans edges of at most $r$ distinct colours. We prove the existence of a
monochromatic triple star with at least $rn/(r^2-r+1)$ vertices in every local
$r$-colouring of $K_n$.
