Yes, it is possible that parsys is in parsys. The overlap issue will be a CSS issue and can be resolved most of the time by adding the following div to the end of your component code.
<div style="clear:both"></div>
In addition, to prevent the addition of additional div styles to your page, this should only be done in author mode:
<% if (WCMMode.fromRequest(request) == WCMMode.EDIT) { %>
<div style="clear:both"></div>
<% } %>
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