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Crump-Mode-Jagers (CMJ) trees generalize Galton-Watson trees by allowingindividuals to live for an arbitrary duration and give birth at arbitrary timesduring their life-time. In this paper, we exhibit a simple condition underwhich the height and contour processes of CMJ forests belong to theuniversality class of Bellman-Harris processes. This condition formalizes anasymptotic independence between the chronological and genealogical structures.We show that it is satisfied by a large class of CMJ processes and inparticular, quite surprisingly, by CMJ processes with a finite varianceoffspring distribution. Along the way, we prove a general tightness result.

Height and contour processes of Crump-Mode-Jagers forests (II): The Bellman-Harris universality class