While a BT will pick up it's own cripples I would think one or more in the squadron would be assigned to transport the more seriously damaged to rear areas for repair or replacement.
At least at high TLs, a Squadron uses to have a single BT, that's why I said a fleet should have some spare tenders just for recovery duties (see also second to last entry in this post).
It is a military axiom to effect repair in the unit if possible, otherwise going no further away than the next able echelon. THIS is where auxiliaries and support ships come into the picture.
And hence my assuming Tenders have nearly full repair capabilities (as long as they are supplied, off course.
Also, while a Battle Tender COULD carry out any of the functions McPerth has described it would be a waste of tonnage as the majority of those functions WOULD be handled by auxiliaries and support ships.
I'm not so sure it is a waste of tonnage, as the Tenders
must accompany your main fleet (assuming BT/BR is the current doctrine, and so TL is high enough), while the auxiliaries cold be left behind to perform the second line and rearguard duties.
Fighters on their own carriers. Escorts, those jump capable, operating as such and not carried.
Tenders use to carry also a nice load of fighters, so carriers could be spared for the main battle fleet (IIRC a Lurenti carries 300 fighters, BRs aside).
Again; Recovery[ATA, ATF, ATS, ATR] Repair [AR, ARS, ARB, ARH, ARV(E), ARV(A)]
Here there's a major difference from wet Navy to Space one (at least in Traveller setting):
In wet navy, a tug (recovery ship) may well tow a supercarrier, albeit at low speeds, as it floats and will follow it (if that's not the case, we're talking about a more complex opperation). SO, recovery ships may be quite smaller than the recovered ships. And if a single tug is not able, you can have more than one towing it.
In Space Navy, to allow the ship to carry (not just tow) a large ship, you need a larger one, as you'd need JD and (more important from size POV) fuel enough for the jump. That means recovery ships must be able to carry the recovered ship as payload, and several ships may not join efforts for it.
A tender must have already this payload, and, (assuming most, if not all, are irregular config) if large enough, it can carry even cruisers of BBs by leaving their BRs, if some form of link may be arranged. (e.g. a tender designed to carry 7 30 Kdton BRs would have the JD and fuel to als ocarry a 200 kdton BB, if it could be linked to it.
A recovery ship designed to carry a 30 kdton BR back to repair if too damaged, OTOH, would be useless if the ship to be recovered is too large.
And in any case, if the ship to be recovered is a Tender, I guess only field repairs (either, by its own crew, by specilalized ships or by another Tender) will aloow it to retreat to a base for further repairs, as I don't envision ships capable to carry them.
[*]I expect them to carry also courriers, either carried into the BT (after all they use to be fairly small) or accompaigning them
Accompanying them with possibly their own Tender.
As those courriers are jump capable, why do you need a tender for them?
I understand a Tender may carry some of them just to have them fueled when arriving to a new system to jump with urgent messages at short notice, but I envision most of them jumping by themselves and refueling with the main fleet.