This is a tail stick spindle for a “T series” Romi Engine lathe. Inside taper is #4 Morse Taper. They are made in three sizes, however exact model of lathe this spindle fits can be only determined by measuring the spindle. Unfortunately no measurements were posted with this listing. My guess is that this spindle fits the Romi T-350 size.

Romi Lathe tailstock spindle. Impossible to tell which model without accurate length and diameter, but it's from CNC turning center with a powered tailstock. The center shaft should be threaded, it'll unscrew (probably left hand threads) from the main barrel.

References:

http://www.romiusa.com/replacement-parts-manuals/

Reason:
Another opinion was accepted instead.

This is a tail stick spindle for a “T series” Romi Engine lathe. Inside taper is #4 Morse Taper. They are made in three sizes, however exact model of lathe this spindle fits can be only determined by measuring the spindle. Unfortunately no measurements were posted with this listing. My guess is that this spindle fits the Romi T-350 size.

References:

http://www.romiusa.com/romi-t-350-2/