Not the dead center. The one with hole that holds the dead center.Are you talking about the "Dead Center" that is stuck in the taper as the picture represents or are you speaking of the Actual Taper and are looking for a way to open up the spindle by removing the tapered portion?
I wasnt aware the taper was a seperate piece within the spindle (if that is what you are saying)! I thought the taper was turned and ground as the inside surface of the spindle bore.Not the dead center. The one with hole that holds the dead center.
More properly described as a "sleeve", I believe. From the illustration, looks like the spindle itself has a taper but there is also a reducing sleeve inside that takes the centre, also with a taper.
-frank