  We study the exponential growth of bifurcating processes with ancestral
dependence. We suppose here that the lifetimes of the cells are dependent
random variables, that the numbers of new cells are random and dependent.
Lifetimes and new cells's numbers are also assumed to be dependent. We
illustrate our results by examples, including some Markov models. Our approach
is related to the behaviour of the Laplace transform of nonnegative additive
functional of Markov chains and require weak moment assumption (no exponential
moment is needed).
