Possible Clues:

• It's not a bit thick that it's herself
• It's not a bit thick that it is a 33 down
• It's a girl! A very thin one, too
• Sneezer's aid
• Organ component
• Tearjerker requirement?
• Kleenex, say
• The children he abandoned may feature in the paper
• Little time to publish paper
• Not a bit thick, so it is, so to take the matter to court