  We consider a neutral haploid population whose generations are not
overlapping and whose size is large and constantly of $N$ individuals. Any
generation is replaced by a new one and any individual has a single parent. We
do not choose the stochastic rule which assigns the number of offsprings to any
individual since results do not depend on the details of the dynamics, and, as
a consequence, the model is parameter free. The genealogical tree is very
complex, and distances between individuals (number of generations from the
common ancestor) are distributed according to probability density which remains
random in the thermodynamic limit (large population). We give a theoretical and
numerical description of this distribution and we also consider the dynamical
aspects of the problem describing the time evolution of the maximum and mean
distances in a single population.
