"it's called DHCP, ricardo. ya may get a different IP address every time ya connect.
the idea is that they aren't all online simultaneously."

It's not dynamic IP as in dial up, the IP is fixed, programmed in the modem and always the same for me.
Even with dynamic IP two DHCP servers from different parts can assign the same IP. The DHCP servers only looks locally at the available free IPs.
I know little about the Internet, so I don't know how it's done for a packet to arrive to the correct IP and not to the other one with the same IP. I think that it is solved with the routers and gateway information.
There's another information, the MAC address that is unique to each network adapter, maybe this information is used locally to deliver the information to the right computer from a trunk sharing the same IP.

Stupidity also evolves!