A lot of tags in RichFaces can AJAX-render elements such as:

<a4j:form>
    <a4j:jsFunction name="updateName" reRender="showname">
        <a4j:actionparam name="param1" assignTo="#{userBean.name}"  />
    </a4j:jsFunction>
</a4j:form>

On the above example, the JavaScript function updateName will AJAX-render the element which has the ID showname.

In some cases, you would have some elements that would AJAX-render without asking them to do so!
I still didn’t figure it out why. (if anybody has an idea, please don’t hesitate to tell me!)

But, I found a way to prevent this!
You simply can add the following attribute to your tag:

limitToList="true"

You even can add it to the tags that don’t have a reRender attribute.
For example:

<a4j:form>
    <a4j:poll id="poll" interval="1000" limitToList="true" />
</a4j:form>