I think the question say it all.
If I deploy some contracts on multiple network in the same deployment. Will they each have a unique address valid on all network or will they each have different address for each network?
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1Depends on your script. If you make sure to use the same account and the same nonce on each network, then they will all have the same address. A contract address is generated based on the account used for deploying it, and the nonce of that account at the time of deployment. – goodvibration Oct 17 '20 at 7:20
