We consider the problem of broadcasting a large message in a large scale distributed platform. The message must be sent from a source node, with the help of the receiving peers which may forward the message to other peers. In this context, we are interested in maximizing the throughput (i.e. the maximum streaming rate, once steady state has been reached). The platform model does not assume that the topology of the platform is known in advance: we consider an Internet-like network, with complete potential connectivity. Furthermore, the model associates to each node local properties (incoming and outgoing bandwidth), and the goal is to build an overlay which will be used to perform the broadcast operation. We model contentions using the bounded multi-port model: a processor can be involved simultaneously in several communications, provided that its incoming and outgoing bandwidths are not exceeded. For the sake of realism, it is also necessary to bound the number of simultaneous connections that can be opened at a given node (ie its outdegree). We prove that unfortunately, this additional constraint makes the problem of maximizing the overall throughput NP Complete. On the other hand, we also propose a polynomial time algorithm to solve this problem, based on a slight resource augmentation on the outdegree of the nodes.