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This paper studies the multicast routing and admission control problem on unit-capacity tree and mesh topologies in the throughput-model. The problem is a generalization of the edge-disjoint paths problem and is NP-hard both on trees and meshes. We study both the online and the online version of the problem: In the offline setting, we give the first constant-factor approximation algorithm for trees, and an O((log log n)2)-factor approximation algorithm for meshes, where n is the number of nodes in the graph. In the online setting, we give the first polylogarithmic competitive online algorithm for tree and mesh topologies. No polylogarithmic-competitive algorithm is possible on general network topologies and there exists a polylogarithmic lower bound on the competitive ratio of any online algorithm on tree topologies. We prove the same lower bound for meshess.