Where did these Rangers come from?

So, there are really only two ways a hockey team can get resources to actually build their team, right? 1. Every season, each team gets draft picks - one per round. 2. Teams can just cold sign undrafted or otherwise unrestricted players. And that's it. Outside of those two methods, all you can do to gain players (or other picks) is trade. And when you trade, you have to give something up: players and/or picks that you already had. So, logically, any player on a team's roster can be traced back, through various trades and draft selections, to some set of that team's originally granted picks and/or unrestricted signings, which eventually led to that player being on the roster.

And so, theoretically, one could trace every single player on a team back to a big set of picks and signings which eventually led to their current roster. Theoretically. (For my purposes, I used the collective roster of everyone the Rangers have had on their official club roster at any point throughout these playoffs.)

Anyway, here's the full list of original pieces that went into the current Rangers' roster.

New York Rangers Draft Picks
1st-round picks: 1986, 1991, 2001, 2004, 2005, 2006, 2008, 2009, 2013, 2014, 2015
2nd-round picks: 1992, 2006, 2008, 2009-compensatory*, 2011
3rd-round picks: 2004, 2010
4th-round picks: 1988, 1997, 2005
5th-round picks: 2015
6th-round picks: 2007
7th-round picks: 1992, 2000, 2014**, 2015***
8th-round picks: 1991

* Compensation for the sudden death of Alexei Cherepanov, the Rangers' 2007 1st-rounder, at age 19
** Pending some unknown condition
*** Pending: only if Ryan Callahan re-signs with the Tampa Bay Lightning in the 2014 off-season

Undrafted Player Signings
Dan Girardi, July 1 2006
Mike Busto, April 27 2007
Cam Talbot, March 30 2010
Blake Parlett, June 24 2011
Ryan Haggerty, March 12 2014

Unrestricted Free Agent Signings
Ray Ferraro, August 9 1995 (terms unknown)
Vladimir Malakhov, July 10 2000, 4 years / $3.5 million per
Mark Messier, July 13 2000, 2 years / $5 million per
Zdeno Ciger, July 17 2001, 1 year / $1 million
Scott Gomez, July 1 2007, 7 years / $7,357,143 per
Marian Gaborik, July 1 2009, 5 years / $7.5 million per
Brad Richards, July 2 2011, 9 years / $6,666,667 per
Anton Stralman, November 3 2011, 1 year / $0.9 million
Benoit Pouliot, July 5 2013, 1 year / $1.3 million
Dominic Moore, July 5 2013, 1 year / $1 million
Mats Zuccarello, July 30 2013, 1 year / $1.16 million

Of course, I have the full list of selections and transactions that turned the above list into our current players, but it's pretty long, and I haven't yet figured out a good way to visualize it. I've been trying to use Microsoft Word to make a giant flowchart, but that's only sort of working, and the text list is naturally unwieldy at best. Maybe I'll post it later? Anyway, the above list comprehensively covers 100% of the assets that eventually became the current Rangers. And now you know!