Deadlock detection in concurrent programs that create networks with arbitrary numbers of nodes is extremely complex and solutions either give imprecise answers or do not scale. To enable the analysis of such programs, (1) we define an algorithm for detecting deadlocks of a basic model featuring recursion and fresh name generation: the lam programs, and (2) we design a type system for value-passing CCS that returns lam programs. We show the soundness of the type system, and develop a type inference algorithm for it. The resulting algorithm is able to check deadlock-freedom of programs that cannot be handled by previous analyses, such as those that build unbounded networks.