We consider the accessibility percolation model on the n-ary tree height the _nite
h. The model is de_ned by associating a continuous random variable X_v for each vertex
v in the tree. The main issue to consider and study is whether or not there is a nearest
neighbor path v_1; v_2; ... ; v_n connecting the root to the tree boundary, such that
X_v1 < X_v2< ... < X_vn. The event de_ned by the existence of this path is called the accessible percolation. In this paper we study the probability of the accessible percolation event. when n is given by n(h) = α(h)h where h is the height of the tree and α(h) is constant. Results are obtained by making h →∞. Additionally, we will discuss other recent results in the literature.