Coming back, late, as usual.
REGISTER
This is a diameter, or face, used as a location. So a register on the Mandrel will be a plain diameter behind the thread for the chuck, usually larger than the thread Not knowing your lathe don't know if it has one.
The Myford ML1,2,3 and 4 did not have a register as such, but their successor the ML7 had a 1.125 x 12 tpi thread with a 1.250 register.
A Backplate would have a short plain bore to locate on the male register on the Mandrel. This will not be more than 0.001 or 0.002" larger than the Mandrel.
Having made a Backplate which locates accurately on the mandrel, it then needs an external register so that it is a close fit in the chuck that is fitted.
The sizes need to be as close as possible to maximise accuracy. If you make a Backplate with a 0.001" clearance on the mandrel, and turn the OD to give a 0.001" clearance in the register in the back of the chuck, even if the chuck were able to hold work absolutely concentric, you could well have work actually running out by 0.002", despite the tight clearances.
Hence it is unlikely that a 3 jaw chuck could hold work absolutely concentric, consistently. Given those clearances, removing and refitting the chuck could well introduce a difference.
If you need two or more diameters to be concentric on a workpiece, in a 3 jaw chuck, you need to turn them without disturbing the work in any way..
With a 4 jaw independant chuck, the concentricity depends up on how accurately you centre the work.
If concentricity is not vital, you can accept run out; but if it is you need to minimise eccentricity.
So, if you were making a simple spacer with a male thread on each end, to hold a plate above another, because of the clearance between the threads and the clearance holes, the two threads do not need to be particularly concentric. With a clearance hole 0.015" larger than the thread, at each end, it probably would not matter if the thread at one end was 0.015" eccentric to the one at the other end.
But if you are fixing two parts so that a shaft can pass between the two, and run easily, the concentricity needs to be better. Assuming a shaft / bearing clearance of 0.004", you would need to hold the two ends of the spacer to no more than 0.002" eccentricity.
That may seem odd, but 0.002 here and another 0.002 there uses up your 0.004 clearance!
In mass production, where several parts have to fit together freely, sizes have be maintained closely (Tight tolerances ) if all parts are to be interchangeable and the device to work as intended.
Tolerances build up. If you were drilling a series of holes and allowed +/- 0.005 on each set of hole centres., after a few holes the tolerance build up might be such that two parts chosen at random may not be able to be fitted together. ( Studs on minimum centre distances trying to fit into holes on maximum centre distances. ten studs could differ by 0.050, and the holes in the opposite direction, giving a total difference of 0.100 )
If, however, you set the holes to distances from one fixed point with a +/- 0.005 tolerance on each distance, every part would fit each other.
Sorry to ramble on, but HTH
Howard