  We consider different disordered lattice models composed of $M$ linear chains
glued together in a star-like manner, and study the scaling of the entanglement
between one arm and the rest of the system using a numerical strong-disorder
renormalization group method. For all studied models, the random
transverse-field Ising model (RTIM), the random XX spin model, and the
free-fermion model with random nearest-neighbor hopping terms, the average
entanglement entropy is found to increase with the length $L$ of the arms
according to the form $S(L)=\frac{c_{\rm eff}}{6}\ln L+const$. For the RTIM and
the XX model, the effective central charge $c_{\rm eff}$ is universal with
respect to the details of junction, and only depends on the number $M$ of arms.
Interestingly, for the RTIM $c_{\rm eff}$ decreases with $M$, whereas for the
XX model it increases. For the free-fermion model, $c_{\rm eff}$ depends also
on the details of the junction, which is related to the sublattice symmetry of
the model. In this case, both increasing and decreasing tendency with $M$ can
be realized with appropriate junction geometries.
