The musicians at the major piazzas are established enough to display CDs for sale. The sidewalk artists paint within a bronze frame secured into the pavement, which makes me think they have an assigned spot. As for the statue artists, although they move about, I believe they have their own official territories. Then there are the artists with an established spot outside the Pitti Palace or Uffizi or along the Arno, who paint and sell scenes of Florence and Tuscany, or who draw caricatures of happy tourists.
If I stop on the street and watch these artists on the street, I always toss a few coins their way.