[155.] In addition to the ordinary ministers there is the formally instituted acolyte, who by virtue of his institution is an extraordinary minister of Holy Communion even outside the celebration of Mass. If, moreover, reasons of real necessity prompt it, another lay member of Christ’s faithful may also be delegated by the diocesan Bishop, in accordance with the norm of law, for one occasion or for a specified time, and an appropriate formula of blessing may be used for the occasion.
So there is a job to do, and the Bishop may appoint laymen to the job. It isn't an Instituted Office, it is a job that is delegated from the Bishop, for a specific time frame.
The kicker:
[156.] This function is to be understood strictly according to the name by which it is known, that is to say, that of extraordinary minister of Holy Communion, and not “special minister of Holy Communion” nor “extraordinary minister of the Eucharist” nor “special minister of the Eucharist”, by which names the meaning of this function is unnecessarily and improperly broadened.
So the Bishop may designate an EMHC, for a specific time frame, at a specific Parish. This permission needs to be renewed. I am not sure if this can be devolved to the Pastor, but I bet that it is that way, in practice.
Romulus is correct there is no such thing as a EEM, there can't be, there may only be an EMHC, for a specific time. It is analogous to the usher, an usher is the usher for only the time he is ushering. One is not ordained an usher, and one can't be ordained an EMHC.