A Key Distribution Center of a network is a server who generates and distributes secret keys used by groups of users to securely communicate. A Distributed Key Distribution Center is a set of servers that jointly realizes a Key Distribution Center. In this paper we study Distributed Key Distribution Centers, pointing out the advantages of this approach to Key Distribution. We propose an information theoretic model of Distributed Key Distribution Center, and present bounds holding on the model. Moreover, we show that a protocol described in [5], which uses Shamir's secret sharing schemes, meets the bounds and is, hence, optimal with respect to information storage, communication complexity, and randomness as well.