Question: Seed phrases seem to be pretty secure, approximately as strong as bitcoin private key according to this site <https://en.bitcoin.it/wiki/Seed_phrase>.

But who store the private key adresses of these seed phrases, I suppose it is the wallet software provider, so each one of these provider have to save this data somewhere, and what prevent them from storing it in clear text and just acting like it didnt know our private key.

Answer: 
The private keys are not *stored*, they are *deterministically generated* from the seed data.

The seed encodes up to 256 bits of random entropy in a human readable form with a checksum attached to it. These details are outlined in BIP39

This entropy is then passed through the PBKDF2 hash function in order to produce a master private key and a chaining key, which are both used to generate further private keys with HKDF-SHA512. These details are outlined in BIP32 - Hierarchical Deterministic Wallets.

When you input your seed phrase into some software which supports these two BIPs, the software will cache the private keys it generates locally, as recreating them each time the software is run would be expensive and inefficient.
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> who store the private key adresses of these seed phrases, 
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The private-keys are generated from the seed-phrase by a mathematical function. There is no need to store a list of seed-phrases and corresponding private-keys.

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> I suppose it is the wallet software provider
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No, you should be the only person to know or store your seed-phrase. Ideally it should not be stored on a computer of any sort. Best practise is probably something like punch it onto metal plates - you can buy [letter punch](https://www.google.com/search?q=letter+punch) kits to help with this. Ideally you'd provide a few trusted relatives with overlapping subsets so that any two of them working together can retrieve your legacy if an airplane lands on you in five seconds from now.