Wallet addresses are NOT ALLOCATED.

So your telling me other peers have no clue about what address is assigned where and there are absolutely no records to prevent duplication?

There're records. But there's no de-duplication. If 2 people generate the same address, they can both spend coins sent there.

So what your telling me is I really do need to write code to generate all possible wallets and I can spend bitcoins out of everyone's wallet?

Yep, exactly.

There's only 2^140 possible addresses! Get cracking!

2^140 = 1393796574908163946345982392040522594123776