NOLO is a French ANR project in which we are interested in the long-time behavior of infinite-dimensional branching processes and in the applications of these limiting results. Such stochastic processes are particle systems where particles move independently according to a Markov process. When a branching event occurs, a particle is replaced by a random number of new particles. Times of branching events, numbers of offspring and offspring locations may depend on the ancestor position. We focus on models with non-local branching: the offspring’s location at birth is chosen through a Markov kernel. Examples are cell division or evolution model. We propose to develop new approaches to prove law of large numbers type results, leveraging ideas from functional analysis, partial differential equation study and probability theory and then derive from those results new statistical estimators.