  We introduce the contour process to describe the geometrical properties of
merger trees. The contour process produces a one-dimensional object, the
contour walk, which is a translation of the merger tree. We portray the contour
walk through its length and action. The length is proportional to to the number
of progenitors in the tree, and the action can be interpreted as a proxy of the
mean length of a branch in a merger tree.
  We obtain the contour walk for merger trees extracted from the public
database of the Millennium Run and also for merger trees constructed with a
public Monte-Carlo code which implements a Markovian algorithm. The trees
correspond to halos of final masses between 10^{11} h^{-1} M_sol and 10^{14}
h^{-1} M_sol. We study how the length and action of the walks evolve with the
mass of the final halo. In all the cases, except for the action measured from
Markovian trees, we find a transitional scale around 3 \times 10^{12} h^{-1}
M_sol. As a general trend the length and action measured from the Markovian
trees show a large scatter in comparison with the case of the Millennium Run
trees.
