Limit law of weighted branching processes

‎In computer science some of the best algorithms are random algorithms with a recursive structure‎, ‎recursive call of the algorithms on a lower level‎. ‎They are special cases of a structure‎, ‎we called the weighted branching process (extension of branching processes)‎. ‎These processes give every individual an abstract weight‎, ‎whereas a branching processes only count individuals‎. ‎We show that the limit distribution of these processes are fixed points of some contraction map‎.