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Bottom brackets cups (Ultra Torque) - No, if torqued (Loctite 22 if hand-tight).
Grease them like every other thread on the bike, with Copaslip as they will usually be going into dissimilar metal BB shells
Crank splines (octalink, HT2, Rotor etc) - ?
Grease them
Bottom brackets bearings (pressfit) - ?
Headset cups (and USA bmx bb cups) -A bit of light oil doesn't do any harm, as with Hirth joints avoid anything with big solid lumps in it.
Bottom brackets cups (threaded - Excluding Ultra Torque) - Yes, grease or antisieze.
Bottom brackets cups (Ultra Torque) - No, if torqued (Loctite 22 if hand-tight).
Bottom brackets bearings (pressfit) - ?
Brake caliper mounting bolts - Yes. SEE BELOW
Brake cables inners when fitting the first time - No (I think light silicon grease is okay, but higher quality cables and housings don't need it at all).
Crank tapers (square) - Yes.
Crank splines (octalink, HT2, Rotor etc) - ?
Headset cups (and USA bmx bb cups) - I don't use any grease when pressing headsets in but I think some do?
Headset bearings (internal etc) - Yes.
Hirth Couplings - No.
Lockrings - Yes.
Pedal / crank interface - Yes.
QR skewer shafts - Yes.
Seatposts (non carbon) - Yes, unless they slip in which case carbon assembly paste.
Seatpost (carbon) - No, use a carbon safe assembly paste.
Stem bolts - Yes.
Track cogs - Yes.
Brake caliper mounting bolts - I think we need some clarification here. "Brake caliper" sounds like a road caliper but "mounting bolts" sounds more like canti/V/disc.
I've never greased any of these. I wouldn't grease the shaft of a road caliper as I wouldn't want it rotating off centre and I wouldn't grease the thread of a road caliper or the bolts for any of the others because these usually have some factory applied threadlock plus I've never come across any of these that I've been unable to undo so I've never felt grease has been needed.