A more descriptive name than what might otherwise be called "total competition".
This is the form of business competitive behavior that I used to tend to think in terms of, but I've since realized that it's highly inefficient and unnecessary. Why compete in market A with another provider when market B is also available and no other provider is there, at least at a quantity, quality, or price level that bests yours.
Note that this is different from PerfectCompetition, but is quite close, in that PerfectCompetition would imply CUAF. but CUAF does not imply PC.
CUAF likely happens outside of PC when firms' owners/managers are too proud to tolerate another firm competing with them. But CUAF could also be modified to reflect the case of competing upon seemingly all fronts, especially when there is imperfect informations about various markets, or, more realistically, relatively more perfect information about one market versus others (in this case, risk aversion and cost would play a key role in determining whether a firm will expand into less information-rich markets).