  We study the influence of the seed graph in the preferential attachment
model, focusing on the case of trees. We first show that the seed has no effect
from a weak local limit point of view. On the other hand, we conjecture that
different seeds lead to different distributions of limiting trees from a total
variation point of view. We take a first step in proving this conjecture by
showing that seeds with different degree profiles lead to different limiting
distributions for the (appropriately normalized) maximum degree, implying that
such seeds lead to different (in total variation) limiting trees.
