Description: We present an analysis of user conversations in on-line social media and their evolution over time. We propose a dynamic model that accurately predicts the growth dynamics and structural properties of conversation threads. The model successfully reconciles the differing observations that have been reported in existing studies. By separating artificial factors from user behaviors, we show that there are actually underlying rules in common for on-line conversations in different social media websites. Results of our model are supported by empirical measurements throughout a number of different social media websites.