Hm, this gets more and more interesting – definitely worthy of some more digging! American Hurtage gives this note on the etymology of the form to do with transplanted buds:

Middle English graften, alteration of graffen, probably from Old French grafier, from graffe, stylus, graft (from its shape), from Latin graphium, stylus; see graffito. N., Middle English grafte, alteration of graffe, from Old French.

http://www.bartleby.com/61/51/G0215100.html


To this, etymonline adds: from Gk. grapheion "stylus," from graphein "write."

Of the corruption (noun) form, AH simply says ‘origin unknown’.