To resolve the question of whether Dick Cheney as Vice President is part of the executive or legislative branch, we solicit wisdom from Extreme Mortman senior historian Richard Andrews.  He offers this:

It’s not either/or.  He’s both.  This is not an unusual concept. 

Many state lieutenant governors are not only state senate presiding officers, but (unlike the VP) have substantial executive responsibilities imposed on them by their state constitution and/or statutes.  These vary greatly.  (I believe there has been a good bit of litigation among the states on the leg?-or-exec? question about lt. govs. The answer is, generally: it depends.) 

A number of them automatically become acting Gov. whenever their Gov. leaves the state.  (Like, famously, California; That always means an interesting time when they are of opposing parties, and the Gov. is trying to run for President.  This happened to Jerry Brown & Pete Wilson.)

Something not addressed in the Washington Post series on Cheney (and that I doubt will be) is that Cheney’s ability to carve out this sort of relationship with “W” is partly based on the uniqueness of Texas.  Bush’s ONLY previous gov’t. experience is being her Governor.  The only kind of #1/#2 relationship he’s had is the one he had THERE.

The Lieutenant Governor of Texas is unquestionably the most powerful in the nation.  On the legislative side, as President of the state senate, he is not merely some once-in-a-while presiding officer; he’s like Maryland’s Mike Miller - appoints all the committees and their chairmen, decides which committee(s) bills will be referred to, establishes the chamber’s “calendar” (agenda), et cetera.  On the executive side he is a member of numerous state commissions & boards that are the  (hydra-) heads of many state agencies, and exercise vast power.  These commissions are not directly answerable to the governor, and to the extent that he appoints their members at all, it is to staggered fixed terms.

Additionally, W was exceeding fortunate to have had a lt. gov. who, even though a Dem., was highly cooperative. 

These two happenstances have necessarily molded the relationship w/Cheney.