Can someone explain how a transmission line starts radiating as the
separation
between the center conductor and ground plane becomes greater and greater.

Ron, A transmission line, by definition does not have a center conductor, and
a ground plane that it reacts with. A transmission line is two close parallel
conductors carrying equal current, but 180 out of phase, so the EM fields
created by each conductor cancels. A transmission line does not radiate.
If you start increasing the spacing between the conductors, then the EM
fields cannot cancel, and according to Maxwell and others, radiation occurs,
you have an antenna. The most efficient radiator is a 1/2 wave dipole, almost
100%.
73 Gary N4AST