Outline stroke from path in Illustrator

I've made a path in Illustrator which I need to be outlined. Quickest way to do this is with Outline Stroke, but then you'll get this united shape (see object in the middle below).

Is there a way to outline a path in a Devide-like way?

I want the object to be like the first cross, instead of the second cross I'm getting with Outline Stroke.

I want the object to be devided so I can easily remove imperfections.

Thanks!