I think it's this section from the pm_newpm template:
HTML Code:
<div class="vbmenu_popup" id="pmrecips_menu" style="display:none; z-index:50"></div>
<script type="text/javascript">
<!--
vbmenu_register('pmrecips', true);
recip_sugg = new vB_AJAX_NameSuggest('recip_sugg', 'pmrecips_txt', 'pmrecips');
<if condition="$show['sendmultiple']">recip_sugg.allow_multiple = true;</if>
//-->
</script>
I believe it's the location of the <div class="vbmenu_popup" id="pmrecips_menu"... </div> that determines where the popup appears.