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Conversation between two people is usually of mixed-initiative, with control over the conversation being transferred from one person to another. We apply a set of rules for the transfer of control to 4 sets of dialogues consisting of a total of 1862 turns. The application of the control rules lets us derive domain-independent discourse structures. The derived structures indicate that initiative plays a role in the structuring of discourse. In order to explore the relationship of control and initiative to discourse processes like centering, we analyze the distribution of four different classes of anaphora for two data sets. This distribution indicates that some control segments are hierarchically related to others. The analysis suggests that discourse participants often mutually agree to a change of topic. We also compared initiative in Task Oriented and Advice Giving dialogues and found that both allocation of control and the manner in which control is transferred is radically different for the two dialogue types. These differences can be explained in terms of collaborative planning principles.