borderVisible="false" should work. You can also try borderAlpha="0". If that still doesn't work, please provide a test case and a screenshot. I am not sure I understand what you mean by "selected asset". Do you mean the border around the entire component? or around the arrow?
Thanks for the response here is a little more information:
<s:DropDownList id="centerSelection" borderVisible="false" skinClass="skins.DropDownOrganizationSkin">
If you click on "headquarters" a popup list display son the right displaying the rest of the options. However I can't seem to get rid fo that border around the component.
If you're using a custom skin, you can just remove the border from your skin right?
I have tried and it still displays border. Even the default skin displays the border. It seems like it is ignoring the borderVisible attribute.
If you want to use the borderVisible style with your skin, you're skin needs to update based on the style's value (see DropDownListSkin.mxml in updateDisplayList()).
I'll need to see your skin to see what's going on.