The development of highly branched inflorescences is considered. Two main characteristics of these structures are the flowering sequences (acropetal, basipetal or divergent) and the branch production (acrotonic, basitonic or mesotonic), which can be different on various branching orders (paracladia). A widespread pattern, found especially among Compositae, is a basipetal or divergent flowering sequence combined with basitonic or mesotonic branch production. We present quantitative models for this type of inflorescence development, based on the transport of a flower-inducing hormone (florigen) and of a hormone responsible for apical dominance (auxin), together with some additional control factors. The computed structures obtained with these models are compared with observations on the inflorescence development of wall lettuce, Mycelis muralis.