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Information floating (IF) is a method of delivering information to mobile nodes in a desired area while avoiding unnecessary communication and information dissemination by restricting direct wireless transmission to a transmittable area (TA). This restriction, however, also leads to the termination of IF, which is a longstanding problem that must be overcome. As a solution, methods have been developed to predetermine the optimal TA size based on environmental parameters such as node density. If the density changes over time, then the estimation of the density and the optimization of the TA must be repeated. Therefore, we previously proposed a method that guarantees that the IF never ends in principle, even if the node density changes over time, by dynamically controlling the TA size. However, this method is only applicable in a one-dimensional network. Here, we propose a method that guarantees, even in two-dimensional networks, that the IF never ends. To accomplish this, we introduce two key functions. The first autonomously restarts the IF even if it has temporarily terminated. The second function dynamically controls the TA size. We also highlight the necessity of introducing a lifetime for the TA generated by the dynamic control method if the density changes over time, and we improve the proposed method accordingly. We show the effectiveness of the proposed methods in terms of continuity and tracking performance through theoretical and simulation evaluations.