Other questions have dealt with where you could find a planet-like object, and what a planet has to consist of to count as a planet. But this question is directed as what orbit or path an object would have to have to count as a planet.
This question was spawned from comments in Does a star need to be inside a galaxy?
We used to think of planets as objects orbiting the sun IAU 2006 Resolution 5A
A "planet" is a celestial body that (a) is in orbit around the Sun [...].
but, depending on how you read
The IAU therefore resolves that planets and other bodies in our Solar System, except satellites, be defined into three distinct categories in the following way
you might think that their definition only applies to our solar system and that they have left open the definition in relation to other parts of the universe.
They were working on what constituted a planet elsewhere IAU Defintion of a "Planet" but they seem to be looking only at the mass and other internal properties of a body, not its orbit (or lack thereof).
Wikipedia quotes these two sources to define a planet as
astronomical body orbiting a star or stellar remnant [...]
That is to say it has extrapolated beyond what its references say to include other single stars. This may be justifiable because
The extrasolar planet issue was deemed too complex to resolve at the 2006 IAU conference (Wikipedia)
but whether it should be restricted to single stars is the question.
It defines a circumbinary planet as
a planet that orbits two stars instead of one
thus contradicting its own monostellar definition of a planet.
On the other hand, it defines a rogue planet by carefully avoiding the use of the term planet
planetary-mass object that orbits a galactic center directly.
So my question is
Are - or should - objects that are in orbit round
- binary (or ternary, etc.) stars,
- galaxy centres, or
be counted as planets?