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I live in the US and I've never sent out an autograph request to the UK before. So, i'm wondering how many british stamps would i need to attach to the SASE for a 8x10 picture?

a 9 x 12 envelope weighing up to 100g (about 3.5 oz) requires postage of £2.07 using the airmail printed papers category.

As Arrowsup says, but to get it back for that price you also need to do the following:

Write "AIRMAIL" and "SMALL PACKET" in the top left hand corner. You want small packet because that covers "a note relating to the contents" as well, which 'printed paper' doesn't (they are the same rate).

You also need a customs form, which I believe you can download from the Royal Mail site. I don't have the link, you'll need to Google it. Print it off and stick it to the front bottom r/h corner, tick 'other', write "photo" for contents, (unless you want to advertise to the world and its postmen who has signed it, "0.1" for the weight, value £0- or however much it cost you to buy the photo - (it might be valuable to you, but to the post office it's just another piece of paper). All that goes on the first line, leave the one at the bottom which says "for commercial items only" blank.

Sign the bottom, leave the date blank.