  We prove a conjecture of W.~Hackbusch in a bigger generality than in our
previous article. Here we consider Tensor Train (TT) model with an arbitrary
number of leaves and a corresponding "almost binary tree" for Hierarchical
Tucker (HT) model, i.e. the deepest tree with the same number of leaves. Our
main result is an algorithm that computes the flattening rank of a generic
tensor in a Tensor Network State (TNS) model on a given tree with respect to
any flattening coming from combinatorics of the space. The methods also imply
that the tensor rank (which is also called CP-rank) of most tensors in a TNS
model grows exponentially with the growth of the number of leaves for any shape
of the tree.
