Can the wire of a high voltage power line be used as the primary coil of an air cored transformer?
This sounds like induction coupling and there is no real theoretical limit to extracting power but the practicalites of "removing" anything more than a few watts are complex. The first thing to remember is that there needs to be current flowing through the overhead wire - it is the current that produces a magnetic field that induces a terminal voltage on a somewhat distant receive coil. 

No current means no stolen power.

It helps if you can use a large inductance "receive coil" because then you stand a chance of tuning it with capacitance to match the AC frequency (50 or 60 Hz). You might get a couple of orders of magnitude increase in terminal voltage by tuning.

But tuning at 50Hz is problematic - the receive coil needs to be largely "air-cored" to be able to gather some of the magnetic field and even if you wound a 100mH coil, at an AC frequency of 50Hz about 100uF is needed to resonate it. Series resistance losses in inductor are going to seriously reduce the Q of the circuit so you might want to use Litz wire.

It can be done but don't expect to power your home lighting from it.