I believe it's called "wrongful detainer".

Or where, if I now bought, would there be a legal argument the occupant was unlawfully detaining my property ?

Yesterday I got a letter from a law firm stating that tenant has retained them to address the unlawful detainer action.

Focus on operating the units, aka getting a good tenant in place who WILL pay rents.The eviction path (Unlawful Detainer action) takes about 90days in Calif and may need to get the Sheriff to come onsite. 

Even if they pay (Remember to accept rents with reservations), go to court the next month if they have not paid the debt in full time the court date, get a UD (Unlawful Detainer) but wave the judgement as you expect them to pay.

Here in San Francisco we post 3 day notices after the lease agreement grace period concludes, and if it doesn't cure we file an Unlawful Detainer and wait for MSC (Mandatory Settlement Conference).

Here is our position from our rental criteria:RESIDENCE/RENTAL HISTORY1.We will examine the most recent five years of residence history.2.Home ownership will be verified through the tax assessors office and/or credit report.3.Rental history will be verified through the property owner and/or rental agent. 4.Rental history reflecting any unpaid past due rent, damages or fees will result in denial.5.Rental history showing excessive property damage, excessive noise, or unruly behavior will result in denial.6.Three or more notices for failure to pay rent and/or to comply with the terms of the rental agreement, within a 12 month period, will result in denial.7.Eviction or unlawful detainer action which has been resolved with full restitution may be approved with additional security deposit.One eviction only.Multiple evictions will result in denial.8.Long term rental history or home ownership is favorable.Residence history that shows an excessive number of moves within the last five years will require additional security deposit.9.If residency was out of state within the last five years, an additional fee may be necessary to conduct an out of state background check.

Hi @Corey Schneider, You will probably need to use the unlawful detainer process to remove the occupants.  

Usually, when you fill out the "unlawful detainer" form at the courthouse, they'll be able to give you an estimate of how long you'll have to wait.  

.* If you do not follow the terms of the “Notice to Pay Rent or Quit” we may then begin eviction proceedings against you and you will be charged with the crime of “Unlawful Detainer” if a judge upholds our claim.