The difference in shape between the observed galaxy stellar mass function and the predicted dark matter halo mass function is generally explained primarily by feedback processes. Feedback can shape the stellar-halo mass (SHM) relation by driving gas out of galaxies, by modulating the first-time infall of gas onto galaxies (i.e., preventative feedback), and by instigating fountain flows of recycled wind material. We present a novel method to disentangle these effects for hydrodynamical simulations of galaxy formation. We build a model of linear coupled differential equations that by construction reproduces the flows of gas onto and out of galaxies and haloes in the EAGLE cosmological simulation. By varying individual terms in this model, we isolate the relative effects of star formation, ejection via outflow, first-time inflow and wind recycling on the SHM relation. We find that for halo masses $M_{200} < 10^{12} , mathrm{M_odot}$ the SHM relation is shaped primarily by a combination of ejection from galaxies and haloes, while for larger $M_{200}$ preventative feedback is also important. The effects of recycling and the efficiency of star formation are small. We show that if, instead of $M_{200}$, we use the cumulative mass of dark matter that fell in for the first time, the evolution of the SHM relation nearly vanishes. This suggests that the evolution is due to the definition of halo mass rather than to an evolving physical efficiency of galaxy formation. Finally, we demonstrate that the mass in the circum-galactic medium is much more sensitive to gas flows, especially recycling, than is the case for stars and the interstellar medium.
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