Connecting to other persons wifi, how much history can they see?

Hi, I am wonder as to how much access people have to internet history when connecting to work/public/other people's wifi. I do not mean what has actually searched via that specific wifi network, but rather whether they can see history searched from the same device at another location and time. So for example is what I searched at home available for them to see when I connect to say, a free wifi cafe network?