Lets use the proper numbers in useful payload , at least proper as far as internet searching maybe someone can come up with the 252 numbers
JU 52 1845kg
C47 3000kg
C46 6800kg
c54 9000kg
It's very difficult to know what these numbers mean, too many books have been written by non pilots and non engineers in which the 'range' of an aircraft is not specified with the standard opperating conditions such as payload being carried and the cruise speed used and the reserves allowed for.
Nor do they note special conditions such as paved runway (which can allow an overload if there are no objects close to the end of the runway)
Using Dave's figures one can say that a Ju 252 can be loaded with 10,932Kg of cargo (non overload) and would then be at its MTOW (Max Take Off Weight) and of course unable to takeoff because it could not carry any fuel. If we remove 932kg of cargo and replace it with fuel we have about 2100lbs of fuel. The Jumo 211 was one of the more efficient piston engines and consumed fuel at about 0.48lbs/hp/hr (less in cases). So the aircrafts total 3 engines of total 4050hp could have been run at full power for over an hour: enough for takeoff and a 220-240mph cruise for about one hour at about 66% power. IE a range of about 200-250 miles. At the other extreme we can immagine the aircraft taking of with say 7 tons of fuel and cruising at 50% power with 2 tons of cargo.
The same applies to the DC-3/C-47
This kind of short range delivery was occaisionally performed.
A particular strength of the Ju 252 seems to have been very good cruise efficiency combined with large fuel capacity.
I did a spreadsheet calculation once of how much fuel, in tons, that it would take to deliver 1 ton of cargo 1000km.
The DC-3 was particularly efficient however the Ju 252 outshone it (bigger airraft better engines). The Ju 52 was not very good though its latter versions were improved. I am working internationally now so can't retrieve my data.
When delivering cargo short distances this fuel efficincy doesn't count too much (say under 300 miles) nor is it critical if a light cargo (passengers with luggage) is taken medium distances to say regional airports with short grass strips. However as distance is increased the fuel demands are a great burden. It may take a ju 252 3.5 tons of fuel to deliver 1 ton of cargo 4000 miles but it would take a Ju 52 about 5 tons, however the Ju 52 would need to do this in 6 hops instead of one and if the Ju 252 was also allowed to split its joourney its efficiency great increases for instance if the Ju 252 does the the journey in two 2000 miles hops the efficiency seems to allow 4 tons of fuel to be used to deliver 5.5 tons of cargo.
this works out at about 1.2 tons of fuel to deliver 1 ton of cargo 4000 miles split into 2.
As I recall I used data from a book called Luftwaffe the allied intelligence files which put standard Ju 252 fuel capacity at 4096kg.
In other works the Ju 252 was 4 times more efficient at delivering a cargo than the Ju 52.
The DC-3 comes across as a good compromise.