  We discuss the scaling properties of free branched polymers. The scaling
behaviour of the model is classified by the Hausdorff dimensions for the
internal geometry: d_L and d_H, and for the external one: D_L and D_H. The
dimensions d_H and D_H characterize the behaviour for long distances while d_L
and D_L for short distances. We show that the internal Hausdorff dimension is
d_L=2 for generic and scale-free trees, contrary to d_H which is known be equal
two for generic trees and to vary between two and infinity for scale-free
trees. We show that the external Hausdorff dimension D_H is directly related to
the internal one as D_H = \alpha d_H, where \alpha is the stability index of
the embedding weights for the nearest-vertex interactions. The index is
\alpha=2 for weights from the gaussian domain of attraction and 0<\alpha <2 for
those from the L\'evy domain of attraction. If the dimension D of the target
space is larger than D_H one finds D_L=D_H, or otherwise D_L=D. The latter
result means that the fractal structure cannot develop in a target space which
has too low dimension.
