I've noticed when embedding an ArcGIS Online webmap which has a popup with links on it, that there seems to be no way to have the popup link open in the current window. It will always open in a new window.
There are no configuration options for link @targets in the ArcGIS Online popup configuration tool and if you try manually setting the target attribute of a popup link to target="_top" or "_parent" that value will be overwritten as target='_blank' and thus links will open in a new window.
This means you can't really integrate the map with your page, because users are taken outside the original window and you have to figure out a way to get them back in.
I wondered if anyone has a workaround and why ArcGIS Online insists on this behaviour?