Take a look at the areas of all the largest land masses on Wikipedia: https://en.wikipedia.org/wiki/List_of_islands_by_area
(in millions of square km, to 2 significant digits)
Africa-Eurasia: 85 (30 Africa, 55 Eurasia (10 Europe, 45 Asia))
America: 43 (25 North, 18 South)
New Guinea: .79
If one takes the actual land masses and ignores the human division into separate landmasses due to isthmuses, then it looks like Australia-Greenland is the best dividing line, at somewhat greater than 3.5 times. America is only just over 3 times as large as Antarctica, and is readily divisible into two separate land masses not much larger than the southern polar continent themselves. But there’s still a big difference between Greenland the next largest islands, not really all that much smaller than the multiplicative difference between Greenland and Australia. After that the islands get smaller much more slowly and there’s no good dividing lines at all other than maybe Sumatra(443k) at around twice the size of Honshu(226k). But Sumatra, Madagascar, Borneo, and New Guinea don’t exactly feel all that more major than Honshu, Great Britain, Sulawesi (Celebes), Java, Luzon (Philippines), Newfoundland, Cuba, Iceland and the two main New Zealand islands, although maybe one could make an argument they are, and should be classified as a “Major Island” or something. Other than some sparsely populated ones in northern Canada that no one cares about, that’s it for 100k km^2 land masses. After that is the second largest of the Philippines (Mindanao), Ireland, Hokkaido, Hispaniola, Sakhalin, Sri Lanka, Tasmania, Terra Del Fuego, and the largest island in the Amazon Delta (Marajo), which are all for 40k or more neglecting more ones in very cold areas no one cares about much. No real lines to draw anywhere there.
I propose the following nomenclature:
Major continents: Africa-Eurasia, America
Middling continents: Antarctica, Australia
Minor continent: Greenland
Major Island: New Guinea, Borneo, Madagascar, Sumatra
But really, artificially separating New Guinea, Borneo, and Sumatra out from Java and Sulawesi seems strange.