Although common ecologists' knowledge has been that the larger the biodiversity of an ecosystems the more stable it is, a result of Robert May in the beginning of the 70s pointed in the oposite direction. May studied the stability of randomly generated ecosystems and found that the larger the biodiversity the smaller the set of the stable ones. For a decade experimental data seemed to confirm this result. However, the improvement of these data and the appearance of assembly models threw away May's result indicating that the selection occurring while building the ecosystem leads to the assembly of a stable community resistant to invasions. In this work we propose a simplified model of an ecosystems that permits us to study the whole assembly process. Such a process generates a finite Markov chain containing all ecosystems connected through invasion. Studying the chain we prove that indeed the assembly process makes the ecosystem more and more resistant to invasions and drives it to an asymptotic robust state. Moreover, such an state is independent on the ecosystem history. In this talk I will describe the model and discuss its properties as well as possible extensions and the insight they will allow us to gain. (http://ifisc.uib.es/~damia/JoseCuesta/assembly_model.ppt.gz)