This control, of course, will appear on the page as a standard <select> control.
In this case, the height of the list after it falls is determined by the browser, and you do not control this. You will notice that when the list approaches the foot of the page, the browser will use the scroll bar as you expected, but not with the number of elements you might want.
My only suggestion was to explore the options offered by some client side dropdown add-ons. You can find some jQuery to help.
A simple Google search for "jQuery dropdowns" gave this article as the main result: 38 jQuery and CSS Drop Down Multi Level Menu Solutions . If you cannot find something here, there are also many similar sites in the search results.
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