Turns out putting the tree top (Christmas Tree Star) is a real problem these days. Our first tree top mount cracked. Bought a second tree top, this one did not come with a mount at all. The third one came with a mount that was way too big and stood out.

Interestingly enough all these tree tops attach with a 5/16" (8mm) rod, so here comes this little adapter: at one end it has an 8mm hole where the tree top goes. The hole is slightly tapered to make up for variations in the rod diameter as well as tighten well when you press the top in. At the other end it has another conical hole - from 8mm (5/16") to 15mm (9/16") diameter, this end goes on the tree. There is also a cut here to give it a bit of elasticity.