An $l$ long $k$-star is a graph with centeral vertex $o$ which is connected to $k$ line graphs of length $l$.

For example a 2-long 3-star looks like:

x1-x1-O-x2-x2
      |
      x3-x3

$o$ is the central node, $x1,x2,x3$ are the three line-graphs connected to $o$.

Rigorously speaking, an $\ell$-long $k$ star is composed of:

1. $k$ line graphs $l_1,l_2,\dots,l_k$ each with $\ell$ vertices
2. centeral vertex $o$
3. $k$ edges $(o,l_1),(o,l_2),\dots,(o,l_k)$

Is there a "standard" name for such a graph family?