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During the OK Computer period, an early lyrical link to the song appeared on radiohead.com :
hotel falling down.
people aware, but not that bothered, as they skate along the shifting surfaces, parisien, huge, blue, grey, metal shine. i am sitting at a table in a destroyed room pushing cocaine around it shines like tiny diamonds. we are smuggling it in white cake
caged birds accept each other.
but flight is what they long for.


During the Kid A era version of radiohead.com, a variation of this text later appeared with the "skating on the surface" bit taken out:


hotel falling down.
people aware but not that bothered.
parisien.
huge.
blue grey steel metal.
people casually avoiding large parts of the structure as it falls to earth.
sitting at a table pushing coke around it shines like tiny diamonds.
In 2004, this image appeared in the Scrapbook section of radiohead.com, raising the question of the lyrics to 'Bodysnatchers' and 'Skirting On the Surface' were at some point related:

'Skirting On the Surface' was one of the titles that appeared on the blackboard the band used during two weeks of rehearsals from september 19th to 30th 2005. At the end of that session, Colin posted a picture of this board on Dead Air Space on september 30th, unfortunately (and probably intentionally) in rather low resolution, so that some of it can't be deciphered:
On October 2nd 2009, the song had its live debut at the Echoplex in Los Angeles as part of the initial touring for the "Atoms For Peace" project. The song was played on three occasions during Thom's solo acoustic section. This is the performance from october 5th at the Orpheum Theatre in Los Angeles:

Radiohead played the song live for the first time ever on march 5th 2012 in Dallas:


Live performances #4 to #6 during the touring for The King of Limbs:
  Unreleased 09/'11 02/'12 march 2012 april 2012 05/'12 june 2012
Identikit [24] 27 29 01 03 05 06 07 09 11 15 09 11 12 14 17 29 31 01 03 05 06 08 10 13
Ful Stop [2] 10 11
True Love Waits [8] 29 29 05 13 18 08 13 15
Cut a Hole [2] 27 03
Skirting On the Surface [3] 05 06 18
'Skirting On the Surface' was not performed during the second half of touring for The King of Limbs.