A holdover action is used if you want your tenant removed whether or not the rent is paid. The will ask for a money judgment for the amount owed but will, primarily, seek possession.
If your building is subject to Rent Control or the Rent Stabilization Code, you may only evict a tenant for reasons and by methods specified in the codes. Similarly, if your tenant has a lease, even if your building is not rent regulated, the lease will dictate the circumstances under which a tenant can be evicted prior to the lease expiration date. Generally these reasons include the following: