If you are using
<input type='text'/>
or
<textarea></textarea>
to display information to a user and do not intend for the user to edit/modify the text box, then you should consider using a label instead.
<label></label>
This will prevent overflow issues and allow the user to scroll to see info as long as other factors aren't preventing scrolling.
If you do need to use a 'textarea' tag then using jQuery you can do:
$("#yourTextAreaId").height( $("#yourTextAreaId").scrollHeight );
Or, if you aren't using jQuery, here is some plain JS for you:
var myTextArea = document.getElementByID('yourTextAreaId');
myTextArea.height = myText.scrollHeight + "px";;
Run either one of those samples after you have set the value of the textarea and/or any time the value of the textarea changes.