You may or may not have "split rims" you almost certainly have multiple piece rims, hopefully they are the two or three piece lock ring type.

This tech tip will explain your possible rims and what you can do. http://www.stovebolt.com/techtips/wheels/

Keeping the three or two piece lock ring wheels and tube type 20" tires is probably your best choice right now.
You probably won't find radial tires that are safe to put on your old rims.

Grigg

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-