Some company that I have no relation to made a deposit into my bank account. If the company does not catch their mistake, does this money become mine? If so how long to I have to wait before I can use this money?
The easy answer is, it won't be yours. At some point the discrepancy will be found. If the amount is sufficient for them to look for, there will be a paper trail and the funds will be taken back from you. "Undue enrichment" says that a person can't expect something for nothing. If it isn't your money, bring it to the attention of your bank so it can be corrected.
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