What is the correct method for removing morse taper tail centers
(Nova), jacob drill chucks from morse taper adapters. Is it buy an
adapter for each item?

I have Oneway tailstock with a #3 taper and I use a #2to#3 adapter to
allow for for use of my #2 Nova live center. However,I find it very
difficult to remove the Nova live center from the adapter. It has a
slot in the adapter that I use a punch to extract the live center.
This appears not to be the right method. as I wind up mucking up the
end of the Nova live center.

Any suggestions?