The mes were originally collected by Enlil and then handed over to the guardianship of Enki, who was to broker them out to the various Sumerian centers, beginning with his own city of Eridu and continuing with Ur, Meluhha, and Dilmun.
This is described in the poem, "Enki and the World Order" which also details how he parcels out responsibility for various crafts and natural phenomena to the lesser gods.
[1] After a considerable amount of self-glorification on the part of Enki, his daughter Inanna comes before him with a complaint that she has been given short shrift on her divine spheres of influence.
The Sumerians apparently considered such evils and sins an inevitable part of humanity's experience in life, divinely and inscrutably decreed, and not to be questioned.
[4] Although more than one hundred mes appear to be mentioned in the latter myth, and the entire list is given four times, the tablets upon which it is found are so fragmentary that we have only a little over sixty of them.