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Those are breadcrumbs. You can completely remove them from all pages by adding the following line into your own layout.xml file.

<remove name="breadcrumbs.container"/>

You can define your own layout.xml file for your module by adding something like the following into your magento modules config.xml

<frontend>
    <layout>
        <updates>
            <namespace_module modules="Namespace_Module">
                <file>namespace_module.xml</file>
            </namespace_module>
        </updates>
    </layout>
</frontend>

Then the layout.xml file would look something like

<?xml version="1.0" encoding="UTF-8"?>
<layout>
    <default>
        <remove name="breadcrumbs.container"/>
    </default>
</layout>