Champions and Their Belts…err “Championships”


Seeing Brock smash Triple H'a World title on Monday's Raw got me thinking.  I know in the past we've seen The Rock and I believe Chris Jericho's trophy cases with titles that they've won.  My question is, are those the actual belts they won?  Does the champion get to keep the belt they won or do they get a duplicate copy from WWE or purchase their own copies? 
And speaking of champions and their "championships," do champions get to travel and take home their belts?  I remember Mick Foley's story when he won the WWE Title and him pulling the belt out as his kids saw him win the thing on TV and also CM Punk's imfamous refridgerator picture.  Do they still get to take home the belts?  And if so, say for example Dolph Ziggler "forgot" to bring the belt with him to Raw, do they have copies backstage?

OK, belts.  I get this one a lot, so let's go over it.
When you win a belt, you get the option of buying a replica copy for yourself, which is what most top tier guys do for the trophy case.  There are actually two sets of belts:  The "hero" belts that you see on TV, and the lower-grade versions that are made to be carried around the airports for house shows.  The higher end TV belts do not stay with the wrestlers and are literally props for a TV show that travel as a part of the set dressing, but on the road, yes, guys will still travel with the crappy road belts.  And yes, they have several copies just in case someone loses it at the airport or leaves it in a cab after a night of partying or whatever.  The exception is the new WWE title, which was apparently so expensive and painstaking to produce that there are only about 3 copies of it made:  The TV version, the road version, and a spare version.