  We show that the structure of a growing tree preserves an information on the
shape of an initial graph. For the exponential trees, evidence of this kind of
memory is provided by means of the iterative equations, derived for the moments
of the node-node distance distribution. Numerical calculations confirm the
result and allow to extend the conclusion to the Barabasi--Albert scale-free
trees. The memory effect almost disappears, if subsequent nodes are connected
to the network with more than one link.
