I am assuming here the tenancy was a month to month tenancy or paid on a weekly basis prior to hold over. If that is not the case you may be able to provide less than a 7 day notice to quit and/or Notice to Terminate Lease. I would do all of the following if possible the more the better 1) hand notice to tenant, 2) post notice securely on the door (take photo of same), 3) send notice to tenant at that location via first class mail. To confirm mailing you could send certified (But not requiring tenant to sign for it). Speak to post office, but you can send letter certified and they will stamp a receipt showing you mailed it, but it does not require tenant to sign for it. You should also be able to print out tracking info from USPS showing it was delivered.
Being conservative you could add 3 days to the 7 notice you mail, but if you hand it to tenant the 7 days starts upon receipt.
After you have waited 7-10 days based on notice then you go to the small claims court in the County where the property is located and request information on filing an ejectment action or simply say eviction and they will know what you are talking about. You should name the tenants as defendants and in the same action file claim for the unpaid rent to date. The Clerk will charge you a filing fee and then also likely charge you the fee on behalf of Sheriff to serve the summons upon tenant. This is not something you do the sheriff or constable will do that for a set fee.
You will be given a speedy Court date likely less than 15 days and you or your attorney must show up or you lose. The same goes for tenants they are required to show up or automatically lose, if they show up they can try and argue some defense. I don't know of one they could argue, but even if the dog died last month and grandma this month, the Judge should typically say I am very sorry you find yourself in this situation, but legally I have no option but to rule for landlord. You could use proof of past rent payments to show the actual reasonable value that you are suing for in addition to possession.
The tenants if they lose will have up to 10 days to appeal and you will as well if you don't like the ruling. The tenants should be forced to post 2 x the value of the judgment on deposit with Court before appeal is valid, but most Courts will allow them to sign a statement saying they are indigent and then the appeal will proceed to the next Court.
If they do not appeal, then after the 10 days has expired you can go back to the same Court and pay them for a writ of possession. The Sheriff or constable will again serve this and it will usually be personally served or stapled to rental and indicate that the sheriff will return usually within a few days and padlock the door. At this point you are required to safeguard the tenants property depending on value for the next 7 days and should send them written notice to the last known address that they must pick up all personal items or they will either be sold or disposed of. To protect yourself I would send this notice to 1) any forwarding address they have provided or 2) to the rental if that is the last known address. I would send this one certified mail return receipt requested and via first class (single stamp). You then have prove that one they signed for the document or two you sent first class mail and it was not returned so it is presumed that it reached them even though they wouldn't sign for the certified mail. As noted this may simply be sent back to the rental if they did not provide you a written forwarding address and did not provide the Court as example in a notice of appeal a new address.
Taking these actions will just protect you from some claim at a later date that you didn't give them notice and then trashed all their property. For the same reason I would ask someone to witness you video the general possessions left behind or write down an inventory before you sale or trash the items.
Here you can read the actual statute that applies http://www.ncleg.net/gascripts/Statutes/StatutesTOC.pl?Chapter=0042 read Article 2A & 3.
I also found this site that might be easier to read https://www.landlordology.com/north-carolina-landlord-tenant-laws/ THIS IS A COMMERCIAL SITE, but it does accurately give you citation back to the state statute that you can read at the earlier link. I wouldn't spend money or paying for a notice to terminate as I can probably find you a sample if you don't want to just Write in about size 24 font (not mandated) that you are hereby given 7 days notice to Vacate the premises due to Holdover.
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