or the distribution of entanglement across a quantum processor often requires circuit depths which grow with the number of entangled qubits. However, in teleportation-based quantum computing, one can deterministically generate entangled states with a circuit depth that is constant in the number of qubits, provided that one has access to an entangled resource state, the ability to perform mid-circuit measurements, and can rapidly transmit classical information. In this work, aided by fast classical FPGA-based control hardware with a feedback latency of only 150 ns, we explore the utility of teleportation-based protocols for generating non-local, multi-partite entanglement between superconducting qubits. First, we demonstrate well-known protocols for generating Greenberger-Horne-Zeilinger (GHZ) states and non-local CNOT gates in constant depth. Next, we utilize both protocols for implementing an unbounded fan-out (i.e., controlled-NOT-NOT) gate in constant depth between three non-local qubits. Finally, we demonstrate deterministic state teleportation and entanglement swapping between qubits on opposite side of our quantum processor.