remove login

I cant understand what do you actually want. Could you attach a screenshot?

The easiest way to do that is to add that line into your local.css file:

   .log-box{

       display: none;

   }

But if you want to remove it from your page open page.tpl.php and remove the block:

<!-- log-box-->
			
			<div class="log-box <?php if ($_GET['q'] == 'user/register') echo 'inversed'; ?>">
                
				 
				 
    <?php if (!$user->uid): ?>
				 <!-- log-box-first --><div class="log-box-first"><div class="left-side"><div class="right-side">
				 <?php echo l(t("Log in"), "user");?>
				 <!-- /log-box-first --></div></div></div>


				 <?php if ($registration_enabled): ?>    	
                 <!-- log-box-second --><div class="log-box-second"><div class="left-side"><div class="right-side">
				 <?php echo l(t("Create new account"), "user/register");?>
				 <!-- /log-box-second --></div></div></div>
				 <?php endif; ?>

	
 	
    <?php else: ?> 

				<!-- log-box-first --><div class="log-box-first"><div class="left-side"><div class="right-side">
				<?php echo t("<strong>!user</strong>", array('!user' => l($user->name, "user"))); ?>&nbsp;|&nbsp;<?php echo l(t("Edit"), "user/" . $user->uid . "/edit");?>
				 <!-- /log-box-first --></div></div></div>


				 <!-- log-box-second --><div class="log-box-second"><div class="left-side"><div class="right-side">
				 <?php echo l(t("Log out"), "logout"); ?>
				 <!-- /log-box-second --></div></div></div>

    <?php endif; ?>



            <!-- /log-box--></div>

After that "Login box" will not be generated any more.