Celestrak has an updated system of categories for retrieving lists of current TLEs, and there's already one for Starlink, yay!
Currently https://www.celestrak.com/NORAD/elements/starlink.txt contains 64 objects from the 2019-029 SpaceX Starlink launch, from
OBJECT A, 44235U, 19029A to
FALCON 9 DEB, 44298U, 19029BR, which appears to be the 60 Starlink satellites plus 4 debris objects from the same launch.
Question: What are these four debris objects? Are any of them the 2nd stage?
click for full size or go to Celestrak elements
TLE eccentricity value versus estimated altitude from mean motion as explained here. Four big blobs around 435 to 440 km are the four debris objects.
plotted using https://pastebin.com/cFLhTJVq