For instance, when IAH opens in Houston or when DFW opens in Dallas. If I were based at either HOU or DAL, would my routes be automatically moved to the new airport when it opens?
Usually you're automatically moved from the old to the new airport, given the new airport is larger. If you wish to remain in the old airport, you have to notify the admin (Sami) well in advance.
I believe the only case where you always need to notify Sami is Tokyo, as both airports are of similar size, but with different demand profiles.
All routes are automatically moved, but it doesn't necessarily means they will be adapted to the new airport. First, there will most likely be a slight difference in distance, meaning each time you edit a route, the times will change (but until then, there's a sort of grace period during which your times remain artificially the same than before). Then, the demand profile might change as well, and some routes might now be without demand, or with much lower demand. And all this if meant to be adjusted manually.
And then obviously, if the old airport closes, you're moved without any need for request (LBG -> CDG).
Relocations without closing include (but not only)
VKO -> SVO
LBG + ORY -> CDG (LBG closes)
DAL -> DFW
HOU -> IAH
HND -> NRT
GMP -> INC
ITM -> KIX
SHA -> PVG
etc.
Actually, a really useful list to keep for future new GW planning. To add to that:
THR -> IKA
It's not quite the same as both close, but don't forget TXL + SXF -> BER. Isn't that one that should be removed for now? Actually, maybe that's the problem with the new BER airport - Sami jinxed it! :P