Re the tee shirt, @Meant2B, it was three years ago, so things may very well have changed, and was from Arts & Sciences. Engineering spent a lot of time with him but no freebies there. I imagine Culverhouse is a hot ticket too, so they probably don’t have as many laying around. 
FWIW, the local recruiting event we attended (even though the kid had already been admitted) had the best swag. My son still wears the free tee he got there. If you’re near a major metropolitan area, I bet there will be one in your backyard. Well worth attending.