First backup your files, following was not tested
I think it´s one way with fewest edits ?
home.htmlFIND & delete
<tr>
<td class="head2" height="20"><img src="{template_url}/images/spacer.gif" alt="" width="4" height="4" />{lang_registered_user}</td>
</tr>
user_loginform.htmlReplace all code with for example
<table width="100%" border="0" cellpadding="4" cellspacing="0">
<tr>
<td></td>
</tr>
</table>
OR
user_loginform.htmlReplace all code with for example
<!-- nothing -->
I don´t know which Style/templates you use(??), but you can make a new template for example
CREATE
login.html{header}
<table width="100%" border="0" cellspacing="0" cellpadding="0" align="center">
<tr>
<td class="bordercolor">
<table width="100%" border="0" cellspacing="1" cellpadding="0">
<tr>
<td class="tablebgcolor">
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td class="navbar" height="23">
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td align="left" width="50%">
<img src="{template_url}/images/spacer.gif" width="4" height="4" alt="" /><font class="navtxt">DüsiPixel Home</font>
</td>
<td align="right" width="50%">
<a href="{url_top_images}"><font class="navtxt">{lang_top_images}</font></a>
<a href="{url_new_images}"><font class="navtxt">{lang_new_images}</font></a>
</td>
</tr>
</table>
</td>
</tr>
</table>
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td width="150" class="row2" valign="top">
<table width="150" border="0" cellspacing="0" cellpadding="0">
<tr>
<td class="head2" height="20"><img src="{template_url}/images/spacer.gif" alt="" width="4" height="4" />{lang_registered_user}</td>
</tr>
<tr>
<td class="tablebgcolor"><img src="{template_url}/images/spacer.gif" alt="" width="1" height="1" /></td>
</tr>
<tr>
<td align="center" class="row1">{user_box} </td>
</tr>
<tr>
<td class="tablebgcolor"><img src="{template_url}/images/spacer.gif" alt="" width="1" height="1" /></td>
</tr>
</table>
{if random_image}
<table width="150" border="0" cellspacing="0" cellpadding="0">
<tr>
<td class="head2" height="20"> <img src="{template_url}/images/spacer.gif" alt="" width="4" height="4" />{lang_random_image}</td>
</tr>
<tr>
<td class="tablebgcolor"><img src="{template_url}/images/spacer.gif" alt="" width="1" height="1" /></td>
</tr>
<tr>
<td align="center" class="row1">
<br />
{random_image}
<br />
<br />
</td>
</tr>
<tr>
<td class="tablebgcolor"><img src="{template_url}/images/spacer.gif" alt="" width="1" height="1" /></td>
</tr>
</table>
{endif random_image}
<p align="center">
<?php
echo date("d.m.Y, H:i");
?>
</p>
</td>
<td width="1" class="bordercolor" valign="top"><img src="{template_url}/images/spacer.gif" alt="" width="1" height="1" /></td>
<td width="18" valign="top"><img src="{template_url}/images/spacer.gif" alt="" width="18" height="18" /></td>
<td width="100%" valign="top"> <br />
<b class="title">Login</b>
<hr size="1" />
<p><br><br><table width="100%" border="0" cellpadding="4" cellspacing="0">
<tr>
<td valign="top" align="left">
<form action="{url_login}" method="post">
{lang_user_name}<br />
<input type="text" size="10" name="user_name" class="logininput" />
<br />
{lang_password}<br />
<input type="password" size="10" name="user_password" class="logininput" />
<br />
<table border="0" cellspacing="0" cellpadding="0">
<tr valign="top">
<td>
<input type="checkbox" name="auto_login" value="1" />
</td>
<td><span class="smalltext">{lang_auto_login}</span></td>
</tr>
</table>
<br />
<input type="submit" value="{lang_login}" class="button" />
</form>
» <a href="{url_lost_password}">{lang_lost_password}</a><br />
» <a href="{url_register}">{lang_register}</a></td>
</tr>
</table><br /><br />
<table width="100%" border="0" cellspacing="0" cellpadding="0">
<tr>
<td>{category_dropdown_form}</td>
<td align="right">{setperpage_dropdown_form}</td>
</tr>
</table>
<p> </p>
</td>
<td width="19" valign="top"><img src="{template_url}/images/spacer.gif" alt="" width="19" height="19" /></td>
</tr>
</table>
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td>
</td>
</tr>
</table>
{footer}
And now you can reach the loginform via "yourdomain.com/index.php?template=login"
or you login via yourdomain.com/admin/index.php
perhaps you have to edit
language/yourlanguage/main.phpFind
$lang['registered_user'] = "Registrierte Benutzer";
Replace with
$lang['registered_user'] = "";
EDIT
On closer examination it seems that removing login box needs a global editing