The question is actually invalid, because both Essendon and Carlton have won the most at 16 premierships each. Therefore, the next team will have won the third most AFL Premierships; and that is Collingwood. The Collingwood Magpies have won 15, but they have lost many more grand finals than they have won!
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Essendon and Carlton: having each won 16/114 contested have the highest percentage of premierhips won, having been in the competition from the beginning.
Collingwood, which has also been in the competition from the beginning, has won 15/114 that have been contested ... and Melbourne 12/114.
So those 4 clubs, among them, have won well over half of all the premierhips so far contested.
Collingwood has played in 43 grand finals (including 2 draws). This is the VFL/AFL record.