Copy and paste shape into Illustrator.
Object > Path > Outline Stroke
With everything still selected, In the Pathfinder Panel, select trim (icon is 2nd row, 2nd on left)
Select the orange parts and delete the unneeded parts
I may not be doing it right.. Seems to remove the lines [borders] and the result is that the separation between the objects is gone - leaving a large blob.
How do I end up with transparency in place of the white lines?
I can get a clean looking logo with the lines removed, by 'selecting colour range' followed by copy and paste, all in photoshop - but when I save it as a png to retain transparent background, the image edges become rough. Is there a step in Pshop that can help me avoid that?
Maybe it's doing as it should until trim. I don't see that selecting orange bits does anything. Am I to use standard selection tool? Selecting in any colour area or specific spots? Sorry to be so dense, but it's not working so far.
seeinghuman: Use the Direct Selection tool in Illustrator. Select just the orange parts and move them away from the white strokes. Then delete the white strokes. Alternatively, you could just select the white strokes and delete them.
You could select the orange parts, copy and paste them back into InDesign, but I'd recommend doing logos in Illustrator and keeping them as an .ai file that you place as needed into your InDesign document. I would avoid Photoshop for logos as Illustrator is much better suited for this task.
In Illustrator CS2, I noticed after the outline stroke function, only the newly created paths remain selected, and the original path is not selected. So, if you select both the new paths and original paths, the pathfinder should be able to do the trim correctly.