  In this paper, we study a class of random walks that build their own tree. At
each step, the walker attaches a random number of leaves to its current
position. The model can be seen as a subclass of the Random Walk in Changing
Environments (RWCE) introduced by G. Amir, I. Benjamini, O. Gurel-Gurevich and
G. Kozma. We develop a renewal framework for the process analogous to that
established by A-S. Sznitman and M. Zerner in the context of RWRE. This
provides a more robust foundation for analyzing the model. As a result of our
renewal framework, we estabilish several limit theorems for the walker's
distance, which include the Strong Law of Large Numbers (SLLN), the Law of the
Iterated Logarithm (LIL), and the Invariance Principle, under an i.i.d.
hypothesis for the walker's leaf-adding mechanism. Further, we show that the
limit speed defined by the SLLN is a continuous function over the space of
probability distributions on $\mathbb{N}$.
