I’ve been looking for this in google or stackoverflow for a couple of hours, before I found out how things work. We are talking about the backend. Lets begin with the Product tabs, because it is easier.

1. Removing Product tabs
a) Open your layout xml file (default: catalog.xml)
b) Search for <adminhtml_catalog_product_edit>
c) Add removeTab action Inside the “product_tabs” block

<reference name="left">
   <block type="adminhtml/catalog_product_edit_tabs" name="product_tabs">
      <action method="removeTab">
          <name>NAME_OF_TAB</name>
      </action>
   </block>
</reference>

You can find out the NAME_OF_TAB, by inspecting the tab’s anchor (<a>) and looking for the “name” attribute.

2. Removing Customer tabs
a) You have to override Mage_Adminhtml_Block_Customer_Edit_Tabs because the Magento guys did a small typo there: they are adding tabs in _beforeToHtml() method instead of _prepareLayout(). So first you have to modify your config.xml and add:

<global>
    <blocks>
        <adminhtml>
            <rewrite>
                <customer_edit_tabs>Yourmodule_Customer_Block_Edit_Tabs</customer_edit_tabs>
            </rewrite>
        </adminhtml>
    </blocks>
</global>

In Yourmodule_Customer_Block_Edit_Tabs just copy and paste the Mage_Adminhtml_Block_Customer_Edit_Tabs contents (don’t forget to change the class name!), and rename _beforeToHtml() method to _prepareLayout()

b) Add the removeTab action into your layout xml (default: customer.xml):

<adminhtml_customer_edit>
    <reference name="left">
        <block type="adminhtml/customer_edit_tabs" name="customer_edit_tabs">
            <action method="removeTab">
                <name>NAME_OF_TAB</name>
            </action>
        </block>
    </reference>
</adminhtml_customer_edit>

Finding out the NAME_OF_TAB is similar as for the products (see step 1).

That’s all folks!