Some philosophers, for example David Lewis, have argued for the need to introduce de se contents or centered contents, i.e. contents of thought and speech the correctness of believing which depends not only on the possible world one inhabits, but also on the location one occupies. Independently, philosophers like Robert Stalnaker (and also David Lewis) have developed the conversational score model of linguistic communication. This conversational model usually relies on a more standard conception of content according to which the correctness (...) of believing a content depends merely on the possible world one occupies. The aim of this paper is to develop a modified conversational score model that operates with centered contents. I begin by explaining how in principle centered contents can figure in the transfer of information from one thinker to another. Here I distinguish the local portability approach from the portable surrogate approach. Then I explain how these modes of information transfer can be exploited in a stalnakerian conversational model involving centered contents, proposing a modified update rule for assertion. (shrink)