1. A computer-implemented method, the method comprising: presenting a user interface having a visual representation for each of multiple ongoing conversations involving a recipient user identity who is associated with each of the conversations; monitoring message activity of the recipient user identity with respect to one or more of the multiple ongoing conversations based on interaction of the recipient user identity with at least one incoming message; identifying activity level associated with at least one of the ongoing conversations for the recipient user identity based upon the monitored message activity; determining a relative hierarchy for the ongoing conversations based on the activity level associated therewith; and arranging the user interface such that a conversation having a relatively high activity level is positioned to reflect hierarchical prominence in comparison to another conversation having a relatively low activity level.