  We define the height process for super-critical continuous state branching
processes with quadratic branching mechanism. It appears as a projective limit
of Brownian motions with positive drift reflected at 0 and a>0 as a goes to
infinity. Then we extend the pruning procedure of branching processes to the
super-critical case. This give a complete duality picture between pruning and
size proportional immigration for quadratic continuous state branching
processes.
