  In this paper, we study a regular rooted coloured tree with random labels
assigned to its edges, where the distribution of the label assigned to an edge
depends on the colours of its endpoints. We obtain some new results relevant to
this model and also show how our model generalizes many other probabilistic
models, including random walk in random environment on trees, recursive
distributional equations and multi-type branching random walk on $\mathbb{R}$.
