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#Remove WP Core update
remove_action( 'wp_version_check', 'wp_version_check' );
remove_action( 'admin_init', '_maybe_update_core' );
add_filter( 'pre_transient_update_core', create_function( '$a',
"return null;" ) );

#Remove plugins update
remove_action( 'load-plugins.php', 'wp_update_plugins' );
remove_action( 'load-update.php', 'wp_update_plugins' );
remove_action( 'admin_init', '_maybe_update_plugins' );
remove_action( 'wp_update_plugins', 'wp_update_plugins' );
add_filter( 'pre_transient_update_plugins', create_function( '$a',
"return null;" ) );

#Remove Theme update
remove_action('load-update-core.php','wp_update_themes');
add_filter('pre_site_transient_update_themes',create_function('$a', "return null;"));
wp_clear_scheduled_hook('wp_update_themes');