Distribute?
2 : i guess you understood something wrong, you will get the money for the game, you won't have to pay the publishers for publishing them.
3 : contact many publishers and ask them for a meeting, talk about your game, your financial expectations, ... and hope they like the game. be sure only a few might be interested, but with a good game and luck, you'll get it published.
4 : if no big publisher wants it, try at some smaller budget-publishers who sell games for 10$ at some supermarkets, maybe they want it.
5 : never pay a publisher for publishing your game, they will get much money and with a bit of luck, you too. they will only get it when they are sure they will make money with it and then it is stupid to pay them.
CU
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Skullpture Entertainment
#40842461