The Zero Emissions Commitment (ZEC), the residual warming after anthropogenic CO<sub>2</sub> emissions cease, remains poorly constrained and directly affects remaining carbon budget calculations. We fit a simple coupled carbon-climate model to ten Earth System Models (ESMs) in the flat10 Model Intercomparison Project. Near-zero multi-model mean ZEC can be decomposed into unrealised ocean warming contributing roughly +0.2 K at 50 years post-cessation, which is almost exactly offset by ~-0.2 K of cooling from atmospheric CO<sub>2</sub> drawdown into land and ocean carbon sinks. Yet the thermal term carries more than twice the inter-model spread of the carbon term; as such, in the context of current ESMs, reducing ZEC uncertainty depends more strongly on equilibrium climate sensitivity and the slow ocean heat uptake timescale than on carbon-cycle parameters. Individual models split into a carbon-dominated majority (eight of ten, negative ZEC) and a thermal-dominated minority (positive ZEC), distinguished primarily by their realised warming fraction and equilibrium climate sensitivity. The simple model yields a compact analytical formula for ZEC in terms of component climate and carbon-cycle parameters, reproducing ESM-simulated values to within ~0.03 K (less than 5% of the ~0.6 K inter-model spread). The decomposition also reveals that the carbon cycle buffers ZEC against uncertainty in committed warming to an existing energetic imbalance: recent downward revisions of the realised warming fraction (the ratio of transient to equilibrium warming) imply substantially more committed warming at fixed atmospheric composition, yet this additional heat is strongly attenuated before it appears in ZEC. A reduction of 10 per cent in the realised warming fraction would increase the radiatively committed warming by ~0.5 K at cessation, but this shifts the 50-year ZEC by only ~0.05 K. This allows potential for process-level constraints on climate and carbon-cycle components on ZEC to narrow carbon budgets. Out-of-sample testing on the flat10-cdr experiment shows that CO<sub>2</sub> predictions diverge from ESMs within ~50 years of the emission trajectory departing from the training rate, so the framework does not extend to full climate reversibility under sustained negative emissions. Structural limitations, including under-sampled land biosphere diversity across ESMs, may further emerge at higher warming levels or on multi-centennial timescales.