Whoa, that chart popped up in the middle of my answering this. I was getting nowhere fast because the numbers weren't adding up. Now I see it's because your explanations of relationship were not clear enough. Z isn't anybody's aunt, she's a younger generation. That was throwing me.
Okay, I'll start over.
So R and N are uncle/nephew and should share 1349-2175 cM. They share 2067, which is in that range.
(If R and N were half uncle/nephew, they would share 500-1446 cM, so we can rule that one out.)
Z and N are granduncle/niece and should share 251-2108 cM. They share 1097, and we're good.
(If Z and N are half granduncle/niece, they would share 125-765 cM, so we can rule that one out.)
R and Z are (on paper) first cousins once removed. They should share 141-851 cM. They actually share zero.
The most obvious explanation is there is a half-sibling relationship going on here. A NPE (non parental event or “not parent expected”) from the sound of it, or you wouldn’t be asking.
But it still doesn’t fit. The half uncle/nephew and half granduncle/niece possibilities don’t come out even close with the numbers.
The only thing I can come up with is that GC has one parent different from N and RH (who are full siblings).
AND that Z is GC’s child, not grandchild.
That would make N and Z half uncle/niece with an expected range of 500-1446 cM, perfect for the actual amount of 1097.
Z and R would be half first cousins and that doesn’t work because the range is 137-856.
I’m at a loss.
Perhaps there was an error when you compared R and Z. I’d put everyone in Gedmatch and check it again.
Note: My cM ranges come from Blaine Bettinger.