It didn't lead very far.
Most of the current roster is made up of players that were acquired via free agency or through the draft. Very few came via trades.
Drafted by the Cubs (6) - Almora, Happ, Baez, Bryant, Schwarber, Contreras
Free Agents (12) - Lester, Farrell, Mazzoni, Duensing, Morrow, Cishek, Chatwood, Rosario, Heyward, Zobrist, Giminez, Darvish
The guys that game through trades were either prospects gained from when the Cubs were flipping veterans 4-5 years ago or were acquired by giving up prospects. Either way leaves a short family tree.
Addison Russell - Jeff Samardzija - draft pick
Kyle Hendricks - Ryan Dempster - free agent
Mike Montgomery - Dan Vogelbach - draft pick
Jose Quintana - Eloy Jiminez (free agent) and Dylan Cease (draft pick)
Justin Wilson - Jeirmer Candelario - free agent
Pedro Strop - Steve Clevenger (draft pick) and Scott Feldman (free agent)
Anthony Rizzo - Andrew Cashner - draft pick
The only player with a family tree that goes any further back is Tommy LaStella....
Obtained in a trade with the Braves for Arodys Vizcaino, who came to the Cubs for
Reed Johnson (free agent) and Paul Maholm (free agent).
Only three branches on this tree, but it is the longest.