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The ultimate fate of (fossil fuel) CO2 emitted to the atmosphere is governed by a range of sedimentological and geological processes operating on timescales of up to the ca. hundred thousand year response of the silicate weathering feedback. However, how the various geological CO2 sinks might saturate and feedbacks weaken in response to increasing total emissions is poorly known. Here we explore the relative importance and timescales of these processes using a 3-D ocean-based Earth system model. We first generate an ensemble of 1 Myr duration CO2 decay curves spanning cumulative emissions of up to 20,000 Pg C. To aid characterization and understanding of the model response to increasing emission size, we then generate an impulse response function description for the long-term fate of CO2 in the model. In terms of the process of carbonate weathering and burial, our analysis is consistent with a progressively increasing fraction of total emissions that are removed from the atmosphere as emissions increase, due to the ocean carbon sink becoming saturated, together with a lengthening of the timescale of removal from the atmosphere. However, we find that in our model the ultimate CO2 sink - silicate weathering feedback - is approximately invariant with respect to cumulative emissions, both in terms of its importance (it removes the remaining excess ~7% of total emissions from the atmosphere) and timescale (~270 kyr). Because a simple pulse-response description leads to initially large predictive errors for a realistic time-varying carbon release, we also develop a convolution-based description of atmospheric CO2 decay which can be used as a simple and efficient means of making long-term carbon cycle perturbation projections. Key Points An ensemble of CO2 pulse emissions are modeled using an Earth system model Our impulse response function projects the atmospheric lifetime of emitted CO2 We characterize how the marine CO2 sinks tend to saturate at very high emissions.