Posto qui, per chi dovesse porsi questa domanda…

codice:
<!doctype html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>Example</title>
<script type="text/javascript">
function autoGrow (oField) {
  if (oField.scrollHeight > oField.clientHeight) {
    oField.style.height = oField.scrollHeight + "px";
  }
}
</script>
<style type="text/css">
textarea.noscrollbars {
  overflow: hidden;
  width: 300px;
  height: 100px;
}
</style>
</head>
 
<body>
 
<form name="myForm">
  <fieldset>  
    <legend>Your comments</legend>  
    

<textarea class="noscrollbars" onkeyup="autoGrow(this);"></textarea></p>
    

<input type="submit" value="Send" /></p>
  </fieldset>
</form>
 
</body>
</html>