What attribute of the table tag controls the table alignment?

The attribute the controls the alignment of a table is the "align" attribute. It's possible values are left, right, and center.

This attribute sets the alignment of the table in relation to the rest of the document.

<table align="center">

....

</table>

This attribute was deprecated in the HTML 4.01. That means that you can use it in HTML 4, and expect it to work in the browsers, but there are better ways of achieving your goal. (CSS)

If you're using HTML 4.01 Strict as your doctype, then use of align is obsolete (meaning the browsers no longer have to support it and its use is prohibited.) The same goes for XHTML 1.0 Strict, and the current draft of HTML 5.

Instead, use CSS margins and floats.