This study deals with a new strategy of the re-assignment for multi-robot seamless coverage tasks using the concept of propagation in a multi-robot surveillance system (MRSS). In the context of MRSSs, multi-robot coverage tasks play a critical role. These tasks require generating paths for two or more robots to cover an entire area, with the objective of minimizing the time needed to complete the task. However, over time, robots may need to be excluded from coverage missions due to issues such as battery charging or malfunctions. It is important to handle these situations efficiently in order to maintain the completeness and balance of the coverage mission. Typically, it can be resolved by either recomputing the coverage algorithm for the remaining robots or redistributing the coverage task of the excluded robot to its neighbors. However, in the proposed method, the amount of coverage area of the excluded robot is equally and efficiently assigned to the remaining robots. First off, a relational graph between robots and a tree based on the excluded robot are sequentially constructed to necessarily know how the robots are geometrically arranged in the given area centered on the excluded robot. The excluded robot becomes the root of the tree, and the depth of the tree indicates the proximity of the coverage areas. Subsequently, the amount of the original coverage area of the excluded robot can be differently assigned to its nearest neighbor robots according to the size of the subtree. Then, the coverage area of the robots corresponding to the second level of the tree are added from the partial coverage area of their parent robot to keep their coverage area balanced, respectively. The similar process is continuously performed, such as 'propagation', until the re-assignment of the coverage area over the leaf nodes is complete. Finally, balanced coverage area is re-assigned to the remaining robots, which is time-efficiently computed. Simulations were performed on two occupancy grid maps that were acquired from a simultaneous localization and mapping method. The proposed method was evaluated against conventional methods on three factors such as the balanced re-assignment of the coverage area (Balancing), the variation of the individual coverage area before and after the re-assignment process (Seamless Coverage), and the total computational efficiency over time (Time-efficiency). The coverage area was uniformly re-allocated after the proposed method was applied. In addition, the proposed method had a short calculation time and enables seamless coverage even after re-allocation. In the future, probabilistic maps related to the importance rate, accident rate, and crowds in the coverage area will also be taken into consideration.