Disable notifications and updates of core Wordpress, Plugins and Themes.

wp_disable_updates.php

<?php 

/*	Disable All WP updates: core, plugins themes and notifications		*/
add_action('admin_menu','wphidenag');
function wphidenag() {
	remove_action( 'admin_notices', 'update_nag', 3 );
}

remove_action('load-update-core.php','wp_update_plugins');
add_filter('pre_site_transient_update_plugins','__return_null');
add_filter('pre_site_transient_update_core','__return_null'); /*remove_core_updates or __return_null*/
add_filter('pre_site_transient_update_themes','remove_core_updates');
?>