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the seller and tenants claim that no leases exist; are there any legal ways to demand written leases?
Yes. If there are no written leases, then the tenant is a month to month tenant. If you are the new owner, then you can require them to sign a new written lease by giving them a new lease and a 30 day notice that it needs to be signed or they would need to vacate. If they don't sign it, then you could consider that a breach of the existing lease contract and then terminate and evict through the courts.
Yes, the existence of a written lease has nothing to do with whether a unit is rent controlled or not. You are still bound by the rent control laws whether they are month to month or whether they are under a fixed term lease.
Under CA law, a landlord can change the terms of a month to month tenancy by providing a 30 day written notice of those changes. So if you wanted to change the terms so as to require a written lease, you just have to give them a written notice stating that 30 days from the date of a letter, you are changing the terms of the tenancy to require a written fixed term lease. The applicable law here is CA Civil Code 827(a) and (b)