Planes have GPS trackers. Not only their company knows where they are, the control center can too. In the case of the north atlantic track system, air control keeps a tight eye on speed, altitude and separation with very precise measurements, even as airplanes are far away from land.
I just fail to see the point of this post. I recently hitched a ride on the cockpit jump seat of a modern airplane for a Europe-East Coast flight and during that I saw the air traffic control knowing exactly where we were, and the pilots communicating via text message (ACARS) with control, as well as using satellite links to contact dispatch (via text messages), as well as satellite phone calls.
Pilots keep paper around them because pilots are there to maintain control, and paper is just another failsafe (with pretty good reliability record!).
Bonus: some planes can notice alterations in the flight dynamics and report an ice buildup. No pilot in this planet is going to let any external person input flight parameters remotely into their aircraft's system while they are in the air.