Magento 1.9 – How to Remove Logout Page

As you want to go back to last page after logout.

Then you need Override to AccoutController.php 's logoutAction.

In magento,you can get Referer Url at any controller using function _getRefererUrl().

Now using _redirectUrl() redirect to this page.

<?php 
require_once Mage::getModuleDir('controllers', 'Mage_Customer').DS.'AccountController.php';
class [ModuleNameSpace]_[ModuleName]_AccountController extends Mage_Customer_AccountController{
 public function logoutAction()
    {
        $session = $this->_getSession();
        $session->logout()->renewSession();
        if(!$session->getBeforeAuthUrl()){
        $session->setBeforeAuthUrl($this->_getRefererUrl());
    }

    $this->_redirectUrl($session->getBeforeAuthUrl(true))
    }

add in your confix.xml in

<frontend>
            <routers>
                <customer>
                    <args>
                        <modules>
                            <company_modulename before="Mage_Customer">Company_Modulename</company_modulename>
                        </modules>
                    </args>
                </customer>
            </routers>
        </frontend>

these is you controller

require_once 'Mage/Customer/controllers/AccountController.php';
class Company_Modulename_AccountController extends Mage_Customer_AccountController
{
    public function logoutAction()
{
    $this->_getSession()->logout()
        ->renewSession();
      //add your code here
    $this->_redirect('*/*/logoutSuccess');
}
}