We consider a model of stationary population with random size given by a
stationary continuous state branching process with a quadratic branching
mechanism.   We give  an exact  elementary simulation  procedure of  the
genealogical tree  of $n$ individuals  randomly chosen among  the extant
population  at a  given time.   Then, we  prove the  convergence of  the
renormalized  total length  of this  genealogical  tree as  $n$ goes  to
infinity, see  also Pfaffelhuber,  Wakolbinger and Weisshaupt  (2011) in
the context  of a constant  size population. The  proof is based  on the
ancestral process  of the extant  population at  a fixed time  which was
defined by  Aldous and  Popovic (2005)  in the  critical case.