Ok.. solved.For those who are interested, means that want to achive publishing shapefiles or (i am quite sure) databases (work too) from ArcGIS Desktop like here http://resources.arcgis.com/en/help/main/10.1/index.html#/Copying_data_to_the_server_automatically_w... (see the image of the 2nd choice: "If the service type you want to publish requires an enterprise geodatabase") to ArcGIS for Server respectively PostgreSQL:1. Do this Tutorial http://resources.arcgis.com/en/help/main/10.1/#/Tutorial_Getting_started_with_geodatabases_in_Postgr... !!Download everything from the Esri Customer Care portal and just use lower case letters for your geodatabase name!! and go until the point "Create a geodatabase" included which for me took 2 hours that it creates the geodatabase. So be patient 🙂2. Connect your created geodatabase to ArcGIS Desktop respectively make a publisher connection to ArcGIS Server from ArcGIS Desktop as described here http://resources.arcgis.com/en/help/main/10.1/index.html#/Making_a_publisher_connection_to_ArcGIS_Se... If you need more info for special configs look here http://resources.arcgis.com/en/help/main/10.1/index.html#/Geodatabase_connections_in_ArcGIS_Desktop/... under PostgreSQL3. Register your created geodatabase respectively the .sde file that was created in the previous step to ArcGIS Server as described here http://resources.arcgis.com/en/help/main/10.1/index.html#//015400000504000000 under the point "Registering ArcGIS Server's Managed Database". Btw where you can find the "Data Store" tab is written at the beginning of this page.4. Publish your services.Cheers