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The default tabs in the customer edit menu are added in the core file

app/code/core/Mage/Adminhtml/Block/Customer/Edit/Tabs.php

To remove the "Shopping Cart" tab, you need to extend Mage_Adminhtml_Block_Customer_Edit_Tabs and override the _beforeToHtml() function without this portion of code:

$this->addTab('cart', array(
    'label'     => Mage::helper('customer')->__('Shopping Cart'),
    'class'     => 'ajax',
    'url'       => $this->getUrl('*/*/carts', array('_current' => true)),
));