Where does Bitcoin run?

Fellow friends,I haven’t seen a clear explanation about this question and I'd love if you could point out for me the right place to research or if not a problem, answer straightforward in here.

Does BTC have a physical server somewhere in the world? We eventually use internet but is there a way to “shut it down” when it really pose as a threat to fiat money? I, person A in Canada, send BTC to you, person B in Australia. After our internet layer, what exactly is the path to make the transaction?

I appreciate any comment, even the funny ones =]