I have an ajaxtoolkit AutoCompleteExtender that has position: absolute. I have placed it inside a div with position: relative. This makes the extender dropdown place itself
Try to add plain HTML <div> element right after extender with spcified id attribute and use this id value for extender's CompletionListElementID property.
When you pass an id to the extender it will insert the items as <div> elements. So adding a plain HTML <div> rather than a <ul> maintains valid HTML.