We wouldn't say 'sponge up', Vincenzo. We would say 'to soak up information like a sponge'.

I agree with Sheena. The only verb phrase including "sponge" that I know is "sponge off + someone". This means rely on someone else financially in an unsatisfactory way e.g. "He sponged off his parents well into his 40s, barely doing a day's work."

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