  Crump-Mode-Jagers (CMJ) trees generalize Galton-Watson trees by allowing
individuals to live for an arbitrary duration and give birth at arbitrary times
during their life-time. In this paper, we exhibit a simple condition under
which the height and contour processes of CMJ forests belong to the
universality class of Bellman-Harris processes. This condition formalizes an
asymptotic independence between the chronological and genealogical structures.
We show that it is satisfied by a large class of CMJ processes and in
particular, quite surprisingly, by CMJ processes with a finite variance
offspring distribution. Along the way, we prove a general tightness result.
