How to improve the transition between a structured and pave

I have a mesh that transitions from structured to pave, and I’d like to improve the transition if possible. Please see the attached picture for reference. Is there anything I can do to improve the mesh growth from the structured region to the unstructured region? I’m able to change the size of the square if that helps anything.

Here is one way to do it. Basically, I meshed the mapped region and then refined the hex sheets based in the desired direction based on a maximum growth factor.

reset
bri x 10
cylinder radius .75 z 12
subtract vol 2 from 1
webcut volume 1 with cylinder radius 4.5 axis z
webcut volume all with plane xplane offset 0 noimprint nomerge
webcut volume all with plane yplane offset 0 noimprint nomerge
imprint all
merge all
compress
vol all size .2
mesh vol 2 4 6 8
refine mesh sheet edge in curve 34 35 51 55 greater_than .3
mesh vol 1 3 5 7

Or, if you don’t want to mess up your mapped zone, just change the size on the paved surfaces to be the size of the outer edges of the mapped zone that way there is no need to transition in element size in your paved mesh. The transition is non-ideal because you are asking for a very large size transition but not giving it enough room.