In this paper, we present a quantum multicasting network, called a generalized quantum connector (n-GQC), which can be used to multicast quantum information from n inputs to n outputs. This network is recursively constructed using n/2-GQCs and consists of O(n log2n) quantum gates. The key component of the n-GQC is another network, called an n-quantum concentrator (n-QC). This concentrator is also an n × n quantum network, and can route arbitrary quantum states on any m of its inputs to its top m outputs, for any m, 1 ¿ m ¿ n. Its quantum gate complexity is O(n log n). The quantum gate-level depths of n-QC and n-GQC are O(log2n) and O(log3n), respectively. Both n-QC and n-GQC are based on the classical self-routing concentrators and generalized connection networks given by Lee and Oruc [1]. While these networks work for multicasting classical packets, they cannot be used to multicast quantum packets as they employ balancer switches with both forward and backward propagation of packets. We introduce a quantum balancer switch that works using a forward propagation of packets only, thereby facilitating the n-QC and n-GQC designs presented in the paper.