Thanks, Babu

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Funny, but we called it the itsy wincy spider, but then I've been known to get the lyrics wrong before.

There are so many variations of the name that it's difficult to say that any particular one is right. I believe the Dutch had their own version.
As far as public domain is concerned, there is no copyright on titles so, as you're probably aware, you can have multiple songs called "Falling In Love Again" (as long as the tunes and lyrics and different). The melody of my "Spider Dance" differs significantly from the nursery rhyme which, by the way, has no known author (according to nurseryrhymecentral.com). I reckon I'm in the clear. wink