I need to show user all autocomplete choices, no matter what text he already wrote in the field? Maybe i need some other plugin?
$('#addressSearch').autocomplete("search", "");
That doesn't work.
There are two scenarios:
You're using a local data source. This is easy to accomplish in that case:
var src = ['JavaScript', 'C++', 'C#', 'Java', 'COBOL'];
$("#auto").autocomplete({
    source: function (request, response) {
        response(src);
    }
});
You're using a remote data source.
$("#auto").autocomplete({
    source: function (request, response) {
        // Make AJAX call, but don't filter the results on the server.
        $.get("/foo", function (results) {
            response(results);
        });
    }
});
Either way you need to pass a function to the source argument and avoid filtering the results.
Here's an example with a local data source: http://jsfiddle.net/andrewwhitaker/e9t5Y/
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