If a nurse had that patient before or they were there the other day and had a specific group of patients, we try to keep the assignments the same where I work. Unless they specifically say they do not want someone back. Sometimes we have patients with such a high acuity that wear you out and nurses ask to not have that patient back. We try to rotate that patients to make it fair, that way one nurse isn't always stuck with that particular patient.
Assignments are typically done by room numbers and we try to keep the rooms as close as possible but when you have a bunch of totals, we tend to split up the assignments. It wouldn't be fair to give a nurse all of the total care patients and everyone else the easier, less acute patients.