Very rough sketch:
My idea is that there are no transaction fees, nor "block rewards". There is an initial amount of coins, and that's it (derived, for instance, from a fork of different existing coins, like bitcoin, ethereum, and a few others). For each address you have on these chains, you are entitled to one coin. Not even proportional. Just a RANDOM initial coin distribution.
This is not going to work. Anyone can generate millions of bitcoin addresses. Even if there is a random amount allocated per address, the one with more addresses gets more coins. They can consolidate all the coins later. So there would be a real mess in the IPO.