The Collaborative International Dictionary of English v.0.48:

Dedimus \Ded"i*mus\, n. [L. dedimus we have given, fr. dare to
   give. So called because the writ began, Dedimus potestatem,
   etc.] (Law)
   A writ to commission private persons to do some act in place
   of a judge, as to examine a witness, etc. --Bouvier.
   [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

DEDIMUS, practice. The name of a writ to commission private. persons to do
some act in the place of a judge; as, to administer an oath of office to a
justice of the peace, to examine witnesses, and the like. 4 Com. Dig. 319; 3
Com. Dig. 359; Dane's Ab. Index, h.t. Rey, in his Institutions Judiciaires,
de l'Angleterre, tom. 2, p. 214, exposes the absurdity of the name given to
this writ; he says it is applicable to every writ which emanates from the
same authority; dedimus, we have given.