Flat bred or NH bred?

*still learning

To answer your question vis a vie whether a Galileo x Annie Power cross would be a NH horse or a flat horse, then more likely a NH horse as Galileo is usually an influence for stamina (he did breed a decent miler called Frankel though).

Its not an exact science though as DANDINO (Dansili x Generous Diana) won over a mile -1M 4F and ran very well in a Melbourne Cup, whilst DOLY CARTE (Doyen x Generous Diana) was a listed winning NH mare over hurdles.  Doyen was a middle distance colt on the flat and Dansili basically a miler IIRC.

Another insomniac on the forum I see!  The simple answer to your question is that it is the intention of the breeder that concludes it. On foal registration the purpose Flat, NH or dual is recorded and totals published annually. Flat breeders aim for precocity in general as races on the flat are for 2 year olds upward. Old fashioned NH breeders want bigger, later  maturing horses with stamina and scope. There is overlap somewhere in the middle. Most colts in both spheres are gelded at some stage as not worth a place at stud. Jumpers, especially over fences, risk a painful experience if they are not.........! Geldings have a better life as they can be turned out in groups, colts and stallions can't.

There is no hard and fast rule.  Generally speaking, foals out of NH mares will be NH-bred.  Most Group 1 winning colts at up to 12f will be marketed as Flat stallions first, then if they fail to make the grade with their first couple of Flat crops they'll either be sold to somewhere like Greece or India, or if they have a bit of stamina in their pedigree will be re-marketed as a NH stallion.  King's Theatre, to use an example quoted upthread, was originally intended to be a Flat sire - he shuttled to Australia for at least a couple of seasons - before connections bowed to the inevitable and focused on the NH side.  Colts who win beyond 12f, like St Leger and Ascot Gold Cup winners, are more likely to be sent straight down the NH stallion route because experience has shown that commercial Flat breeders won't touch them with somebody else's bargepole.  You'll get the odd one advertised as "dual purpose" from the outset, which is stud-marketing-speak for "probably going to be sh!te at both".

Sadler's Wells was dual purpose in fact but never in intention or marketing. No one sending a mare to him, or to Galileo or Montjeu, would have been hoping to breed a Cheltenham Festival winner (in the same way as Frankie Dettori wasn't hoping to get a QMC winner when he sent his mare to Dubawi).  He just had a lot of stock that didn't make the grade hoped for them on the Flat or that their breeding would have suggested they were capable of - Istabraq's dam also produced Derby winner Secreto to SW's sire Northern Dancer, for example, so three CHs wasn't on Hamdan Al Maktoum's mind when he bred him - but who were sound enough and classy enough to make decent hurdlers in particular.

There is more money and quicker returns in Flat breeding than NH, so if there is even a small chance of a horse making it as a Flat stallion, that's usually what its connections will go for at least at the start of its career.

If the produce Group winners on the flat they remain flat sires.  If they produce sprinters they remain flat sires.