Because of the AC current flow, there is a changing magnetic field around the conductor, that in turn induces a changing electric field and vice versa
But does the EM radiation get "loose" from the conductor and propagate through air like with a dipole antenna for example or is it fixed around the conductor getting weaker with distance?
Since the summ of all currents in the distribution network is zero, then the magnetic fields caused by each conductor cancells out. The complete cancellation however occurs at infinite distance. But looking practically they cancel in close vicinity, some hundreds of meters from the powerline.
Since the poweline is not an antenna it does not irradiate the EM power. Like you have mentioned a dipole, it's a setup with two wires going in opposite direction. It also has to be matched, for example dipole has to be half wavelength, you can do a small calculation how distant it would need to be.
To sumarize your question: The field is arround the conductor, only. It does not propagate through the air as antenna. If you look at Maxwell equations, then this is so called near field region.