Using a set of zoomed-in cosmological simulations of high-redshift progenitors of massive galaxies, we isolate and trace the history of gas that is accreted by central supermassive black holes. We determine the origins of the accreted gas, in terms of whether it entered the galaxy during a merger event or was smoothly accreted. Furthermore, we designate whether the smoothly accreted gas is accreted via a cold flow or is shocked upon entry into the halo. For moderate-mass (10^6 - 10^7 Msun) black holes at z ~ 4, there is a preference to accrete cold flow gas than gas of shocked or merger origin. However, this result is a consequence of the fact that the entire galaxy has a higher fraction of gas from cold flows. In general, each black hole tends to accrete the same fractions of smooth- and merger-accreted gas as is contained in its host galaxy, suggesting that once gas enters a halo it becomes well-mixed, and its origins are erased. We find that the angular momentum of the gas upon halo entry is a more important factor; black holes preferentially accrete gas that had low angular momentum when it entered the galaxy, regardless of whether it was accreted smoothly or through mergers.