An experiment with a very good barrel showing how groups go very wild as soon as the head-to-bore relationship crosses a criterion where the head is of a size that allows in-barrel yaw; whether during loading or during travel down the barrel (as Travis suggests and Aj implies);
25 yards groups and discussion. All groups are of 5 shots.
Here the skirts are all sized to 4.52 mm or pretty close to groove size.
The middle group has the head at 4.47 mm and the lands are compatible with the fit.
The top group, same skirt but heads of 4.44/4.45 mm - the group is starting to spread.
Bottom group - same skirts but heads of 4.43 mm and things are wild. Expect that when your bore is over-sized to some criterion degree, regardless of choke.
Now to find the barrel's tolerance for head size and to show that it is not so much skirt size, providing the skirts are at least groove size:
These groups had skirts from 4.53 to 4.66 mm (recall groove size was 4.52 mm).
Heads were 4.50 mm top and bottom groups; 4.51 mm left group. There is little to pick in group size between these and the middle group above with heads of 4.47 mm.
However we see that at 4.44 / 4.45 mm the group was beginning to spread a little and then at 4.43 mm top target bottom group and then 4.41 mm, bottom target middle group, group size has suddenly exploded.
Further testing has confirmed that, for this barrel, head sizes from groove size at 4.52 down to 4.46 mm groups are excellent, with my preference going to the median size of 4.49 / 4.50 mm but anything from 4.46 to 4.52 is digested. Above groove size of 4.52 heads are too big and again it is very difficult to introduce them to my own barrels without the loading pressure inducing some yaw.
Barrels which have had chambers and leades specifically machined to allow progressive centering of heads and skirts can, I think, be tailored to shoot over-sized (fractionally) heads acceptably.
I hope my experiment has been of some interest and is found to be relevant in the context of this thread. ... Regards to all, Harry. (Some spelling corrected)