  We first identify (up to linear isomorphism) the Lipschitz free spaces of
quasiarcs. By decomposing quasiconformal trees into quasiarcs as done in an
article of David, Eriksson-Bique, and Vellis, we then identify the Lipschitz
free spaces of quasiconformal trees and prove that quasiconformal trees have
Lipschitz dimension 1. Generalizing the aforementioned decomposition, we define
a geometric tree-like decomposition of a metric space. Our results pertaining
to quasiconformal trees are in fact special cases of results about metric
spaces admitting a geometric tree-like decomposition. Furthermore, the methods
employed in our study of Lipschitz free spaces yield a decomposition of any
(weak) quasiarc into rectifiable and purely unrectifiable subsets, which may be
of independent interest.

Metric Geometry;Functional Analysis