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Please consider this scenario. I agree with other party that we will create 2/2 multisig wallet, so we can only spend funds from that wallet together. The other party will create its wallet, generates first key as her/his own (public+private) and then imports my public key as second key. That is correct 2/2 multisig wallet.

But I will create 2/3 wallet on my side. I will generate two own keys and as third key I will import public key of other party. That means I can use only my own keys to fully sign the wallet.

Will both wallets see funds when one of us will deposit? In theory I could then withdraw funds only myself, because I have necessary two keys of three, while other party things the wallet is 2/2. Or will these be two different wallets?

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No, when a receiver generates an address, the address instructs the sender what scriptPubKey to assign funds to. A scriptPubKey commits to specific spending conditions. The scriptPubKey for a 2-of-2 will be different than for a 2-of-3. When the money is sent to the 2-of-2 address, it can only be spent by an input that satisfies the given spending conditions, in that case, a 2-of-2 OP_CHECKMULTISIG with exactly the two original public keys in the order as originally determined.

Further, only wallet software looking for the original 2-of-2 will recognize the output as its own.

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