NH and OZ F awards are pretty easily available from NA to Asia if you book in advance. There's sporadic availability in between, and pretty good availability within 2 weeks of departure, though not as predictable as LH. NH has low YQ these days and is one of the best F products in *A.

TG F has pretty good availability year-round as well. Some routes like NRT-BKK on the A380 seem to only be available T-14, while other A380 routes can be found far in advance or close to departure.

LH F starts to become available in the T-14 window, but often more like T-1 to T-5 for tougher routes. Some routes are easier than others. Generally if you see 5 or 6 unsold seats when that window opens there's a pretty good chance a seat will become available eventually. Some destinations are near impossible to score an award seat on because of high paid demand (e.g. HKG, SIN, JNB, LAX, SFO)

SQ F is available only to CGK and BWN last I checked (I've also seen BOM and DEL at some points)

AI F is also available year-round, but I haven't tried it yet, so can't comment.

CA F used to have good availability from North America, but that seems to have all dried up as of late (plus AP has difficulty seeing CA award space.)

UA F is not worth your time. Even AC J is better IMHO.