Hi, Spinner size and aerodynamics is very complicated. Just look how radial engine cowlings developed from fairly simple Townend type rings to complex integrated cowlings with intricate baffling, internal streamlining and complicated exit cowl flaps. The Spinners grew from little caps on the hub to become large aerodynamic forms that matched the cooling flow. Some even used additional cooling fans, not to mention the hollow spinners.
For the Liquid cooled engines there is the obvious streamlining of the prop hub but then, the aerodynamics of the engine installation and the rest of the airframe come into the picture.
The single engined fighter has a particular issue with the top lines of the cowling WRT the pilot's forward view and sightline. Generally, there is a conflict in aerodynamics where the best pilot view requires a good high position to sight over the nose, against the high thrustline of many upright inline V-12's. IMO, the spinner size on many Merlin powered fighters was limited by its high thrustline and the need to have a sightline over the nose. In the Hornet for example, it appears that the larger spinner was worth using aerodynamically because the cowl could be higher over the engine to give a larger spinner backplate diameter.
The relatively lower thrustline of the inverted V-12's is interesting. Early Bf 109 versions used a small spinner with a very close fitting cowl that maybe had a small cross section area but seems quite angular. The sightline over the nose is so close to the top of the engine that the engine actually cuts through the top of the cowl at the front of the crankcase.
With the Bf 109 F onwards, Messerschmitt was able to greatly increase the spinner backplate diameter and use a large aerodynamic spinner, without raising the top cowling line more than a few millimeters (it still almost touches the front of the crankcase).
Similar observations could be made of the Fw 190 D and Ta 152, where they were able to actually use annular radiators because of the low thrustline, while still having a fair sightline. Of course, the spinners for those aircraft are not as large but, the annular radiators are quite advanced.
Cheers
Eng