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Is this file you reference a bitmap or a vector? If a vector then there whould be no background that cannot be deleted. If a bitmap then you must create a vector of the edge and us it as a clipping path.
It is a TIF file, when loaded into Photoshop it has a Transparent background
but when I place it in Illustrator it has a white background (Iwant to put it on a yellow oval) and I havenot a clue how to make the background transparent.
in Photoshop, go to the help menu, select "export transparent background wizard", follow the few easy steps. & you will have an .eps file that you can place over yellow or anything else.
What the "wizard" does is just to create a vector path & then create a mask with it like Fred suggested. It is often a rather crude "path", so, you may need to work harder making a better path, but it is very handy for designing when you want to see the results, or get client approval before working harder.
There are a few ways to get the edge of the graphic but you are going to make a mask in Illustrator.
As Fred siad you can create a vector edge in Illustrator or Photoshop.
In Photoshop you can select the backround color with the wand, make the selection a path and then export that path into Illustrator, or another way is depending on it's use and version of Photoshop, "Save for Web" has transparent options.
In Illustrator you can hand draw the edge, or you can try and vectorize the logo and select the edge for making the mask.