abstract: The phenomenon of time and spatial evolution of growing networks is often appearing in the field of life sciences, ranging from biology related examples, blood vessels expansion in the human body or plant’s invasion of the soil through roots spread, to network of social interactions between individuals. In this work we focus on the hyphal growth in the filamentous fungus Podospora anserina, and propose a stochastic model for their spreading mechanism at the microscopic scale. The growth of new branches is driven by a field of nutrients, absorbed by the network itself. Creation of new branches is also considered as well as merging of an existing branch into another one. A deterministic PDE is then obtained as macroscopic limit for the density of the network, both in space and velocity variable.