Hi WS -
The procedures for obtaining a ZED ticket are up to each employing airline. For some, like AA, the employee and anyone else eligible for ZED tickets, can walk up to any AA ticket office to request a ZED. At other airlines there are centralized offices that manage this and usually require that the employee submit a request on behalf of himself and anyone of his dependents that wishes to travel. I'm not sure at all what UA's procedures are.
As for accompanied vs. not accompanied status, the ZED agreement has no restriction on travel by a spouse or dependent child traveling with out the employee. UnlessUA has agreed to a restriction on a bilateral basis you should be able to travel without your spouse on any of the airlines with which UA has a ZED agreement.
Hope this helps and happy traveling!
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