minimal effect on admission, which is very numbers-based, but i would argue a somewhat sizable affect on performance and recruiting.
people from top ugrads come into law school more confident, more "scholarly", and with much larger social networks (ex at HLS, around 10% of the class is from Harvard undergrad alone). So they get tips from upperclassmen, get outlines, stuff like that.
For something like 1L internship when there are hardly any grades out, the only criteria employers can use is what you did before law school. Which undergrad, which internships, etc. so here a top-name school will help out alot. For 2L recruiting the effect certainly goes down, but firms are still happy to go for people with better pedigree and likely more impressive 1L internships. that said, a 2L from a state school with rockstar grades will great recruiting-wise.