I would say that bmiRegional fit in no way with cityFlyer, which operates from LCY only, bar some summer charters from MAN and Scotland. It may be possible that a SunAir type franchise in BA branding, but all commercial responsibility with Granite may be possible, at least in the interim.
Baby, on the other hand is a different kettle of fish. Although LCC operations from UK regional airports is not the remit of BA, IAG do have an established (albeit smallish) European LCC player in Vueling, who are now entering the UK market via CWL. It may well be that Baby could end up as part of Vueling UK. For all its flaws, Baby does have a decent niche in the Midlands and potential in Northern Ireland. I feel it is likely that IAG will end up with baby, by hook or by crook and in that scenario would be likely to turn it over to Vueling.