jQuery UI inside widget on admin page

Ok, so, for some reason I can’t comprehend, the answer is that the div element containing the tabs should have a class and not an id for jQuery UI to work properly, as such:

<div class="mytabs">

and

jQuery(document).ready(function($) {
    $(".mytabs").tabs();
});

Just for the record, the way I enqued the scripts is:

add_action( 'admin_enqueue_scripts', 'load_my_admin_js' );

function load_my_admin_js($hook){
if( 'widgets.php' != $hook )
        return;         
wp_register_script( 'my_adminjs_script', plugins_url( '/adminjs.js', __FILE__ ), array('jquery','jquery-effects-core','jquery-ui-tabs'));
wp_enqueue_script('my_adminjs_script');
}

Perhaps the problem was a combination of the two points above.. Anyway, it now works