Explaining "barrels regulation"...
Let me give it a shot (pun fully intended)
The two barrels should shoot together, right? Whether "together" means shots touching, 1" apart, 2" apart, etc. can be discussed endlessly, but it seems that for DG hunting out to 50 meters/yards with iron sights, 2" groups are OK.
On DG doubles built for .500 case-head (that includes most .400, .450, .465, .470, .475, .476, .500), the two barrels are about 1" apart, bore center to bore center, at the breech, so one would think that if they stayed parallel, 1" apart, bore center to bore center, all the way to the muzzle, the two barrels would shoot parallel into eternity, right?
That is almost, but not quite 100% true with the over/under rifles because both barrels recoil in the same vertical axis as the rifle stock grip, and almost the same vertical axis as the stock (depending on stock cast). Therefore, recoil is essentially in straight line and there is no sideways yaw. This is why O/U doubles rifles are easier and cheaper to make, and much less sensitive to ammo variations (bullet weight, bullet bearing surface, velocity, etc.), and when changing ammo with them, most of the changes are addressed with replacing the front sight to move the point of impact (POI) higher or lower to the point of aim (POA).
Where the side by side doubles are different, and the bigger the caliber, the more pronounced the difference, is that neither barrel is in the same vertical axis as the stock grip and stock. The left barrel is left of the stock, and the right barrel is right of the stock. What this means is that the left barrel pulls the rifle left under recoil, and the right barrel pulls the rifle right under recoil. This is the "yaw." The two shots diverge under recoil. Always. How much to the left and to the right? It depends how long the bullets take to go through the barrels (bearing surfaces, velocity, barrels length, etc.), hence how long the recoil lasts, and how much recoil and yaw there is (caliber, bullet weight, velocity, powder charge, etc.).
The only way to get the two shots "together" is for the two barrels to mechanically converge when assembled. The typical .470 will have about 1" distance bore center to bore center at the breach, and about 0.75" distance bore center to bore center at the muzzle. The barrels clearly converge. This is an easy-to-verify fact.
The art of barrels regulation is to have the two barrels converge just enough when soldering the front wedge between them, so that the convergence of the barrels compensates exactly for the divergence of the shots under recoil. In a perfect world, the barrels convergence at the muzzle would be just so, and the rifle would shoot two parallel trajectories and the two shots would never cross nor spread.
This would be the ideal world, but this is not the real world, if only due to the fact that no two shooters get the same group from the same rifle, because no two shooters control recoil exactly the same way and keep the rifle from yawing left then right exactly the same way.
In the real world, the process of barrels regulation means soldering the front wedge between the barrels/shooting/unsoldering and moving the wedge/resoldering the wedge;
... and again shooting/unsoldering and moving the wedge/resoldering the wedge;
... and again shooting/unsoldering and moving the wedge/resoldering the wedge;
... and again, and again, etc. until the result is deemed good enough.
Good enough is not the same for each gunmaker. Good enough is when the gunmaker meets his goal (whichever that goal might be) and calls it quit. The less expensive the double, the faster this time comes. Push time savings - understand: costs savings - to its limit, and some makers try to replace the "solder/shoot/unsolder" process with blind soldering of a CNC machined wedge, and there is no predicting what group size the rifle will shoot, and where it will shoot it. Enter the infamous Dremel to start altering the crowns and push bullets right or left as they leave the barrels...
The really good regulators get the barrels close to shooting parallel, but very rarely do they shoot perfectly parallel, so all doubles will tend to cross (at 50 meter/yard? 75? etc.) or they will tend to spread (1" group at 25 meter/yard, 2" at 50? 3" at 75? etc.). This is just the nature of the beast. And that is the day the rifle was regulated, with the ammo lot used, and with the shooter used... Then the sights are adjusted so that the point of impact (POI) covers the point of aim (POA).
Now, add to that, even when shooting the exact same bullet with which the rifle was regulated, some differences in powder lots, temperature of the place (Africa vs England or Germany), barometric pressure (altitude), humidity, shooter form, shooter's ability to control recoil and yaw, shooter fighting the recoil or rolling with the recoil, etc. and most doubles fired by most shooters will not shoot parallel and their shots will either converge or diverge.
In the old days, the British gunmakers regulated their doubles to cross at 50 to 65 yards in England because cordite developed higher pressure in warm Africa than in cold England, so when the rifles were shot in Africa, the higher pressure caused more recoil. More recoil caused more yaw and divergence when shooting, and the crossing at 50 to 65 yards either moved to 100 yards, or maybe was replaced by spreading at 100 yd, which was fine enough for any real world application.
In the old days too, the British gunmakers also insisted that the rifle be shot during regulation by the client himself, so that the clients's unique way of controlling recoil and yaw would be built into the regulation. When they built for clients with considerable experience (e.g. professional ivory hunters) they built a little less convergence into the regulation because these guys knew how to control recoil and yaw. Conversely, rifles for first time safari clients usually had a tad more convergence, because it was likely that the rifles would yaw a little more under recoil.
So, in summary, there is no hard rule for what is regulation of double rifles, because the results will change with the same rifle shooting differently for different shooters, even with the same load. Never mind with different loads. In the real world, a rifle is very well regulated in my view when it keeps 2 shots from each barrel of its regulation load in a 2" group anywhere between the muzzle and 50 yards. And, realistically, 3" is OK too in my view. Whether this group at 50 yd has the two left shots on the left of the group (no crossing - preferable) or on the right of the group (crossing likely around 40 yd and starting to spread at 50 yd - less desirable), is essentially OK too as long as one does not try to group this rifle at 100 yd. And this will change when the shooter changes bullet shape, load, powder lot...
Developing the loads a fraction of a grain at a time to increase or decrease the amount of yaw (recoil energy) and the time the bullet spend in the barrel (velocity) will increase or decrease the divergence of the shots between recoil, and will bring the rifle into the convergence built into the way the wedge was soldered.
Sorry, this is again probably too long of a post, but this is not an easy subject to compress into just a few sentences...
I hope this answered the questions
