The Collaborative International Dictionary of English v.0.48:

Ex parte \Ex` par"te\ [L. See Ex-, and Part.]
   Upon or from one side only; one-sided; partial; as, an ex
   parte statement.
   [1913 Webster]

   Ex parte application, one made without notice or
      opportunity to oppose.

   Ex parte council, one that assembles at the request of only
      one of the parties in dispute.

   Ex parte hearing or Ex parte evidence (Law), that which
      is had or taken by one side or party in the absence of the
      other. Hearings before grand juries, and affidavits, are
      ex parte. --Wharton's Law Dict. --Burrill.
      [1913 Webster]

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

EX PARTE. Of the one part. Many things may be done ex parte, when the
opposite party has had notice; an affidavit or deposition is said to be
taken ex parte when only one of the parties attends to taking the same. Ex
parte paterna, on the side of the father, or property descended to a person
from his father; ex parte materna, on the part of the mother.