I have discovered 3 black walnuts of about 3 years of age and about 5 feet high growing very close together... i am digging them out. Is their any information about how deep the tap root goes...? or how about some information about what type of fertilizer they need. i am residing in the south western portion of new mexico.

If you do transplant them wait until the winter when they are dormant?

deeeeep tap root. need to be dormant when you dig

Black wlanuts are extremely slow growing and have very deep tap roots.
If you want them to live, leave them in place. Transplanting nut trees doesn't work very well in my experience.