The appointment of an (auxiliary)bishop is by the decree of the Holy Father and the Bishops' Congregation. With the appointment, the designated obtains "ius ad rem", which means a right to the office and rights and obligations associated with the office although he can only exercise these rights on canonical transfer of the office (in this case consecration as auxiliary Bishop of Linz) ( "ius exercendi"). As Father Wagner has not yet received episcopal consecration, he is not yet bearer of the associated ecclesiastical Office. With the lawful appointment by the Holy Father, Father Wagner has firstly the right and the duty to receive Episcopal consecration and to take over the office. In principle seek from the Pope the withdrawal of the nomination - not from the Office which he is still not arraigned with. This must be in writing and be a free decision.
If you are the messages of different news agencies give faith that Wagner did not receive a written request for resignation to the Holy Father has sent, then pastor of the Wagner Act did not set. There is no canonical resignation attempt from him. The request is simply non-existent. The act of the withdrawal request must be in writing for it to exist externally, according to the legal rule: "Quod non est in Actis non est in mundo", ie: What is not recorded in writing, is not.
Canonically, everything is as provisional as it was: Wagner is appointed Auxiliary Bishop of Linz. By being so, he remains ” ius ad rem," with a right to the Office and its rights and obligations. Only when the Holy Father is presented with a written request, the Pope, taking into account the circumstances in Austria and church has been satisfied in consideration of the consequences that of such a papal act for the world, will the resignation decision be confirmed.