In this paper we rewrite Wang's Minimal-Connected-Component (MCC) model  in 2-D meshes without using global information so that not only the existence of a minimal path can be ensured at the source, but also such a path can be formed by routing decisions at intermediate nodes along the path. We extend this MCC model and the corresponding routing in 2-D meshes to 3-D meshes. It is based on our early work on fault tolerant adaptive and minimal routing  and the boundary information model  in 3-D meshes. We study fault tolerant adaptive and minimal routing from the source and the destination and consider the positions of the source and destination when the new faulty components are constructed. Specifically, all faulty nodes will be contained in some disjoint faulty components and a healthy node will be included in a faulty component only if using it in the routing will definitely cause a non-minimal routing path. A sufficient and necessary condition is proposed for the existence of the minimal routing path in the presence of our faulty components. Based on such a condition, the corresponding routing will guarantee a minimal path whenever it exists.