8
The fieldset does create the block line you describe. If you look at the code here for theme_blockcenter_c.html
<div style="padding: 5px;">
<fieldset>
<{if $block.title != ""}><legend class="blockTitle"><{$block.title}>legend><{/if}>
<div class="blockContent"><{$block.content}>div>
fieldset>
div>
the line is created by 'fieldset' you can simply remove the tag as follows ...
<div style="padding: 5px;">
<{if $block.title != ""}><legend class="blockTitle"><{$block.title}>legend><{/if}>
<div class="blockContent"><{$block.content}>div>
div>
or as studioC described add an attruibute in the CSS.
If you are not seing these changes, I think you need to clear templates_c and make sure your theme is set to update in admin preferences.