  We solve the growing asymmetric Ising model [Phys. Rev. E 89, 012105 (2014)]
in the topologies of deterministic and stochastic (random) scale-free trees
predicting its non-monotonous behavior for external fields smaller than the
coupling constant $J$. In both cases we indicate that the crossover temperature
corresponding to maximal magnetization decays approximately as $(\ln \ln
N)^{-1}$, where $N$ is the number of nodes in the tree.
