The Large TextArea is a rather extreme example, but it shows how it adjusts for styling.

The grey dotted line is there to show the real textarea. Except for font and line-height, style the container, not the textarea.

For IE, it helps to specify the font-family for textarea.

If things aren't working as expected, use development tools like Firebug to inspect the textarea and its shadow and make sure the computed styles match.

Here are the styles used in this page:
textarea {
  font-family: sans-serif;
  padding: 0;
  margin: 0;
} 
DIV.small {
  padding: 5px;
  width: 300px;
  border: 2px solid #999;
}
DIV.large {
  padding: 10px;
  width: 300px;
  border: 2px solid #999;
}
DIV.small textarea, DIV.large textarea {
  border: 1px dotted #eee;
}
DIV.large textarea {
  font-size: 20px;
  font-weight: bold;
  line-height: 1.5em;
}

AutoSizingTextArea Demo

Small TextArea

Large TextArea