[Aragorn]

Cats spray usually to mark territory. Cats will usually spray if they feel threatened (see other cats outside/inside), want to attract a mate or feel imposed on. You can try and prevent spraying in cats by having them "fixed." You may want to close the curtains so they can't see other cats. I have had indoor cats for years and the only time they marked was when they saw other cats outside.

Even though you will be cleaning the carpets of your new house, that will not remove all traces of the smell (and potential marking spots.) Urine migrates to the floor underneath, and the only sure fire methods I have found are removal of the sub-floor and/or encapsulation. Once it gets to the wood, the smell will always be there until it is removed or encapsulated.