tokens: Figure A1. A convergence study of the evolution of the mass of dense gas with n ≥ n cloud /3. For all cloud sizes the three highest resolution levels show good agreement, especially at early times t ≲ 5 t cc , implying that these simulations are well converged. At the same time, the low-resolution simulations with R cloud /Δ x = 76 (dashed lines) systematically differ from the other simulations. Thus, only the dense gas survival mass fraction in the 2D simulations with R cloud /Δ x ≥ 152 are converged. The evolution of the number of FoF groups for the 2D simulations is shown in Fig. A2 . We confirm the conclusion that clouds with R cloud ≫ l cool undergo excessive fragmentation for a resolution of R cloud /Δ x ≥ 152. Only the low-resolution simulations with R cloud /Δ x = 76 are not capturing this result in 2D. Figure A2. The number of FoF groups in 2D simulations with a resolution of 607, 304, 152, and 76 cells per cloud radius (from left to right). For R cloud /Δ x ≥ 152 the 10 and 100 pc cloud simulations have a higher peak number of FoF groups in comparison to the non-radiative and 1 pc cloud simulations. A resolution of R cloud /Δ x = 76 is evidently not enough to cause fragmentation of a 100 pc cloud since the peak N FoF value is comparable to the 1 pc simulation with radiative cooling. We conclude that a resolution of R cloud /Δ x ≥ 152 for our 2D simulations is sufficient to capture fragmentation in 1, 10, and 100 pc simulations with cooling. A2 3D simulations Because 2D and 3D clouds may be affected differently by instabilities, we carry out the same resolution studies for the 3D simulations. First, we remind the reader that the dense gas mass survival fraction studied in Fig. 1 behaves very similar for our low- and high-resolution 3D simulations, with the only notable difference being that the dense gas in the 100 pc simulation at low resolution survives longer in comparison to the high-resolution simulation. To further study convergence properties we show the evolution of N FoF in Fig. A3 . The figure confirms that the 10 and 100 pc simulations are more fragmented than the non-radiative simulation and the 1 pc simulation with radiative cooling. Overall, this confirms our result that clouds larger than the cooling length shatter to smaller cloudlets. However, the figure also shows that fragmentation of the 100 pc cloud in 3D is not fully captured, because the 10 and 100 pc clouds here have a similar number of FoF groups throughout the simulations. This conclusion is further supported by the evolution of the power spectral slope of the low-resolution simulations shown in Fig. A4 because the peak value of the slope is not larger in the 100 pc simulation in comparison to the 10 pc simulation. Excessive fragmentation of the 100 pc cloud in comparison to the 10 pc cloud is thus only seen in our high-resolution 3D simulations. Figure A3. N FoF as a function of time for the low-resolution 3D simulations (with R cloud /Δ x = 80). The
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