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Fig. C.1

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Core composition during oligarchic growth at 3 au with a heavy initial disk. The upper panel shows Case-2, where only water is accreted. As a result, the rock mass fraction, which is the initial model, decreases. The lower panel shows Case-3, where 50% water and 50% rock is accreted. As all the rock directly reaches the core, but the water can evaporate in the envelop, the core always has a rock mass fraction above 50%. The water that is added to the core can either directly reach the core (dark blue regions) or be added because the envelope was saturated (light blue).

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