  We study a random recursive tree model featuring complete redirection called
the random friend tree and introduced by Saram\"aki and Kaski. Vertices are
attached in a sequential manner one by one by selecting an existing target
vertex and connecting to one of its neighbours (or friends), chosen uniformly
at random. This model has interesting emergent properties, such as a highly
skewed degree sequence. In contrast to the preferential attachment model, these
emergent phenomena stem from a local rather than a global attachment mechanism.
The structure of the resulting tree is also strikingly different from both the
preferential attachment tree and the uniform random recursive tree: every edge
is incident to a macro-hub of asymptotically linear degree, and with high
probability all but at most $n^{9/10}$ vertices in a tree of size $n$ are
leaves. We prove various results on the neighbourhood of fixed vertices and
edges, and we study macroscopic properties such as the diameter and the degree
distribution, providing insights into the overall structure of the tree. We
also present a number of open questions on this model and related models.
