Peer-to-peer networks provide better scalability for the filesharing applications they underlie. Unlike traditional server-based approach such as FTP, maintaining a constant QoS with a fixed number of servers seems feasible, whatever the number of peers involved. However, a P2P filesharing network sometimes happens to saturate, notably in a semi-P2P filesharing architecture or during flashcrowds phase, and scalability may fail. Even "smart" networks can encounter the whole file but one piece downloaded case, which we call starvation. We suggest a simple and versatile filesharing model. It applies to all pieces-oriented filesharing protocols used in softwares such as MlDonkey or BitTorrent. Simulations of this model show that starvation may occur even during flashcrowds. We propose a theoretical explanation for the so-called starvation phenomenum.