Based on what I read a couple of years ago, I think that they sold-off the Auto Centers (or, at least some of them) several years ago.
In NJ, a mega-dealership purchased a few of the "Sears" Auto Centers a few years ago, and I can tell you from my personal experiences about 2 years ago that the closest "Sears" Auto Center is apparently not owned by Sears.
I wanted to get a free load test done on my battery, and for many years, Sears Auto Centers had featured free drive-in load tests. There was always one bay door that was kept open, and you could--literally--just drive up to the desk where they dealt with load tests and battery replacements. On this occasion, there were no open bay doors.
So, I parked my car, and ventured into their Auto Center's retail store, which I immediately noticed to be...VERY...different from how it used to appear. I approached the nasty woman at their service desk, inquired about a load test, and was told that there would be a minimum 2 hour wait for a load test, and that it would cost $19.95.
I declined her generous offer, and drove to my nearest Auto Zone, where they immediately performed a free load test of my battery.
The way that Sears management is selling-off the company's assets is just too similar to the ways of the Roman soldiers who vied for Jesus' possessions...