If we're discussing the frontend of the website, the particular line you've asked about....
<?php echo $this->getChildHtml('content') ?>is added to the Magento layout XML in app/design/frontend/base/default/layout/page.xml. In Magento version 1.8, you'll find it defined in lines 92-94.
<block type="core/text_list" name="content" as="content" translate="label">
<label>Main Content Area</label>
</block>By looking at the "type" attribute of this block tag, we can know what object class this section of the layout is. It comes from the "Core" module, and is of the block type Text List. The class name for this Mage_Core_Block_Text_List. (app/code/core/Mage/Core/Block/Text/List.php). Text Lists are simply block containers which purpose is to store additional child blocks inside them. You can add any number of child blocks to the text list and they will be rendered out either in the order they were added or the order they've been assigned.
So, to answer your question, there is no view script (.phtml file) that renders the contents of $this->getChildHtml('content'). The blocks which have been added to this block, may themselves have view scripts associated with them. To find out what view scripts those are, you'd have to find the layout XML which has added the block.
For example, if I had the following layout file added to the frontend of my website's theme:
<?xml version="1.0"?>
<layout>
<default>
<reference name="content">
<block type="core/template" name="my_view_script" template="hello/world.phtml" />
</reference>
</default>
</layout>The code above, would add the block with an object class of Mage_Core_Block_Template to the block with the name 'content' (which happens to be the one you asked about). Magento will then look for the view script in the following locations, in this order:
app/design/frontend/PACKAGE_NAME/THEME_NAME/template/hello/world.phtml
app/design/frontend/PACKAGE_NAME/default/template/hello/world.phtml
app/design/frontend/base/default/template/hello/world.phtml First one that is found, is the one it will use. If no view script is found Magento will log an error in var/logs/system.log (default log file setting) stating that the view script was not found. No output from the block will occur.
Note that depending on your settings in System -> Configuration -> (General) Design, there may be additional package/theme locations Magento will look in. There are also other scenarios such as if the "Custom Theme" is field is changed for individual CMS Pages, Catalog Categories, or Catalog Products, these individual model's view page may have an additional view script location (that will match the selected theme) that takes precedence over your site's default settings.
Magento will follow this same fallback logic when looking for translation files as well as layout XML files.
Please note, that it is perfectly acceptable to copy individual view scripts (avoid copying entire directories, copy over only view scripts you actually intend to modify) from app/design/frontend/base/default/template/ to your local theme, and customize them for the purposes of your website's theme. However, in order to have an upgrade compatible site, layout filesshould not be copied from base to your local theme. Doing so, does not follow upgrade compatible practices. Instead, XML Layout updates for your theme should be contained in app/design/frontend/PACKAGE_NAME/THEME_NAME/layout/local.xml. There is no layout instructions from app/design/frontend/base/default/layout/*, that cannot be removed/added-to/changed, what-have-you, with the proper XML instructions in local.xml.
What does it refer if no argument passed? ie <?php echo $this->getChildHtml() ?>
When no string argument for a block name is passed to <?php echo $this->getChildHtml() ?> then all child blocks of $this will be rendered in order. Even if they've already been output higher up in the same view script