I'm watching the progress of a new office building being built over the road (essentially a manual timelapse).
The way the building progressed was by the pouring of a concrete core in the centre of the building to the full height (~8 storeys), before a steel beam frame was constructed around it to the full width/length of the building, obviously making a frame for the outer walls and floors.
Although the core is substantial (not just a pillar or something), it wouldn't seem to have any structural effect on the outer parts of the floors of the building (near the outer walls).
My lay-person's guess on the purpose of the core is as a kind of protected fire space (dry-risers? wet-risers?) containing the stairs and lifts/elevators, but if I knew the answer I wouldn't be asking here.