I solved this by replacing text in search text box and replacing keydown function search action...
Here is code:
//Function to Change default behavior of SearchBox
function FixSearchBox() {
var theSearchBox = $('#SearchBox input');
var defaultSearchText = "Search this site";
var preferredSearchText = "Search everything";
var SearchCenterUrl = "/sites/search/";
theSearchBox.val(preferredSearchText);
theSearchBox.attr("title", preferredSearchText);
theSearchBox.blur(function () {
if ($(this).val().indexOf(defaultSearchText) > -1)
$(this).val(preferredSearchText);
});
theSearchBox.focus(function () {
$(this).val("");
});
$("#SearchBox input").attr("onkeypress", "");
$("#SearchBox input").keydown(function (e) {
if (e.keyCode == "13") {
ProcessClick($("#SearchBox a[title='Search']"), preferredSearchText, SearchCenterUrl);
}
});
}
//Function for starting search
function ProcessClick(button,preferredSearchText, SearchCenterUrl) {
var query = $("#SearchBox input").val().replace(preferredSearchText,"*");
var selectedSearch = $("div.ms-qSuggest-hListItem").text();
if (query.length < 2 || query == '*') {
document.location.href = SearchCenterUrl +"/Pages/results.aspx?k=*";
}
else {
switch (selectedSearch) {
case "People":
document.location.href = SearchCenterUrl + "/Pages/peopleresults.aspx?k=" + query;
break;
case "Conversations":
document.location.href = SearchCenterUrl + "/Pages/conversationresults.aspx?k=" + query;
break;
case "Video":
document.location.href = SearchCenterUrl + "/Pages/videoresults.aspx?k=" + query;
default:
document.location.href = SearchCenterUrl + "/Pages/results.aspx?k=" + query;
break;
}
}
}
PS. I added also a thing to search for '*' if you just click on search action (search icon).
to remove "Search this Site" from drop down I used css:
div.ms-qSuggest-listItem:last-child
{
display:none;
}