Branching extremals of the functional of $\lambda$-normed length

Networks on $\lambda$-normed planes are considered, that is, on normed planes for which the unit circle is a regular $2\lambda$-gon. A geometric criterion is given for an arbitrary tree to be extremal on the $\lambda$-normed plane, where $\lambda\ne2,3,4,6$. Problems of $\lambda$-minimal (extremal) realization of an arbitrary network and of convergence of $\lambda$-extremal networks as $\lambda\to\infty$ are also considered.
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