A little conference history.
BYU and Utah were in the same conference from 1932 until 2011 (Skyline/WAC/MWC).
Utah, BYU, Arizona, and Arizona State were in the WAC together from 1962 to 1978.
Utah, BYU, and TCU were in the WAC together from 1996 to 1999.
Utah, BYU, and TCU were in the MWC together from 2005 to 2011.
So, there is a lot of conference history between BYU, Utah, Arizona, and Arizona St. and some conference history between Utah, BYU, and TCU.
And, here's how many games the 3 remaining corner schools have played against Big 12 or potential Big 12 schools:
Arizona: 96 Arizona St., 47 Utah, 33 Texas Tech, 25 Colorado, 25 BYU
Arizona St.: 96 Arizona, 33 Utah, 28 BYU, 13 Colorado
Utah: 96 BYU, 69 Colorado, 47 Arizona, 33 Arizona St.