Generally speaking (which means this doesn't hold true in all situations), a Smartzone system's control channels won't rotate. A Smartnet system's control channels will rotate. I'm not an expert on this, so this may be completely incorrect. I'm sure others who are more knowledgeable will correct me if necessary.
My understanding is that when programming a subscriber radio for a Smartzone system, one has to program in each possible active control channel frequency, but radios are limited in the number of available memory slots. I think it used to be 32 control channel frequencies, maybe now it's more like 64 (or more). For a system like Palmetto 800, with 62 sites, each with a primary control channel and at least one alternate, that's as many as 124 possible frequencies (some sites "advertise" more than one alternate according to trunker, and there is some frequency duplication state-wide, so that number is approximate). If the control channel for each site rotated among 3 or 4 frequencies, that's a lot more frequencies to program (200+).
In a Smartnet system, you're allowed to program up to 4 control channel frequencies for each system. So those rotate on a more regular basis. Examples of Smartnet systems in SC would be Florence, Charleston City, Horry County, Sumter County, Beaufort County and many Business SMR systems. Charleston County is actually a simulcast single-site Smartzone system. Asheville NC is upgrading their Smartnet system to a Smartzone system right now.
Based on my observations in the Upstate, the control channels on Palmetto 800 sites don't change often. Paris Mountain changes more frequently than the others, maybe once a month for a day or less at a time, and I think that's due to interference. When Motorola is testing a site, they can also manually change the control channel.
Hope that helps.
Brian