Bifurcations play a major role in the evolution of landscapes by controlling how fluxes such as water and sediment are partitioned in distributary and multithread channel networks. In this paper, we present the first experimental investigation on the effect of the downstream boundary on bifurcations. Our experiments in a fixedwall Y-shaped flume consist of three phases: progradation, transitional, and bypass; the first two phases are net depositional, whereas during the third the sediment flux exiting the downstream boundary matches the input on average. We find that deposition qualitatively changes bifurcation dynamics; we observe frequent switching in the discharge partitioning under net depositional conditions, whereas bypass results in long periods of time where one branch captures most of the flow. We compare our results with a previously developed model for the effect of deposition on bifurcation dynamics. The switching dynamics we observe are more irregular and complex than those predicted by the model. Furthermore, while we observe long periods of time where one branch dominates under bypass conditions, these are not permanent, unlike in the model. We propose that the range of switching timescales we observe arises from a complex interplay of downstream-controlled avulsion and the effect of bars in the upstream channel, including previously unrecognized long-Term dynamics associated with a steady bar. Finally, we describe bifurcation experiments conducted with sand but no water. These experiments share the essential feedbacks of our fluvial bifurcation experiments, but do not include bars. In these experiments, we find that the sandpile grows symmetrically while it progrades, but bypass leads to one branch permanently capturing all avalanches. We conclude that the downstream control of deposition vs. bypass is likely a major influence on bifurcation dynamics across a range of physical systems, from river deltas to talus slopes.