The progression of mobile technology in recent years has opened up new issues for the development of mobile applications dedicated to mobile devices such as iPhone, Andoid and Windows Phone. Consequently, the adaptation of existing desktop applications with these devices becomes a necessity. However, this adaptation is a challenging problem as they do not have the same features. Operational transformation (OT) is one of the best techniques for supporting collaboration using mobile devices; it is used by Real time collaborative editors to allow several users to edit the same shared document simultaneously. However, the collaborative editor OT-based log can grow without bound as more and more updates arrive and new users join the group; this will eventually exhaust the available storage at a site and particularly if the site is a mobile device. In this paper, we propose a novel design of distributed based-log garbage collection scheme for peer-to-peer and mobile network; it optimally manages mobile devices resources and improves the performance of desktop real time collaborative editor's application by optimizing log size.