How to plant a merger tree

We investigate several approaches for constructing Monte Carlo realizations of the merging history of virialized dark matter haloes ('merger trees') using the extended Press-Schechter formalism. We describe several unsuccessful methods in order to illustrate some of the difficult aspects of this problem. We develop a practical method that leads to the reconstruction of the mean quantities that can be derived from the Press-Schechter model. This method is convenient, computationally efficient, and works for any power spectrum or background cosmology. In addition, we investigate statistics that describe the distribution of the number of progenitors and their masses as a function of redshift.