The Internet development and the availability of reliable networks led to the emergence of Grid architectures. The aim of these architectures is to take benefit of widely distributed resources to improve execution possibilities. Depending on their properties, these architectures are usually classified into desktop grids, resources grids and application based grids. Application based grids provide an easy access to applications deployed on the grid on the ASP (Application Service Provider) mode. When these grids grow of orders of magnitude, application lookup will become a costly activity of the grid. In this article, we study how a lookup algorithm scales when the size of the grid grows up. We exhibit a "lookup throughput" which characterizes the grid interconnections graph and the lookup algorithm.