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Could anyone please help me and tell me what is the name of the font used for the writting on this.

Looks like ITC Tapioca.

http://www.identifont.com/show?3FK

Is there any other font that kind of looks like ITC Tapioca but has smooth edges.

ITC.Tapioca is like it is. How close you you want it to look like? Just the same sort of feeling or is there any particular letter that would be a reference for a lookalike?

i'd like it to look close to the tapioca just not jagged like it i'd like it to be smooth. you can give me afont with the same feeling as well.

Have a look at [ulr=http://www.google.es/search?hl=en&client=firefox-a&rls=org.mozilla%3Aen-US%3Aofficial&hs=rB6&q=%22kidstuff.ttf%22&btnG=Search]kidstuff.