The propagation of Analog Single Event Transients (ASETs) to multiple outputs of Bipolar Junction Transistor (BJTs) Integrated Circuits (ICs) is reported for the first time. The results demonstrate that ASETs can appear at several outputs of a BJT amplifier or comparator as a result of a single ion or single laser pulse strike at a single physical location on the chip of a large-scale integrated BJT analog circuit. This is independent of interconnect cross-talk or charge-sharing effects. Laser experiments, together with SPICE simulations and analysis of the ASET's propagation in the s-domain are used to explain how multiple-output transients (MOTs) are generated and propagate in the device. This study demonstrates that both the charge collection associated with an ASET and the ASET's shape, commonly used to characterize the propagation of SETs in devices and systems, are unable to explain quantitatively how MOTs propagate through an integrated analog circuit. The analysis methodology adopted here involves combining the Fourier transform of the propagating signal and the current-source transfer function in the s-domain. This approach reveals the mechanisms involved in the transient signal propagation from its point of generation to one or more outputs without the signal following a continuous interconnect path.