First post and apologies for asking questions of matters the answers to which are probably obvious to everyone but me.
Last night (5 April) I flew without checked baggage to HKG, from MNL on a PQ flight. I had a an award booking on a CX flight some 4 hours later. Both flights obviously on discrete tickets. On approaching the CX transfer desk I was told that they (the transfer desk), could not issue a boarding pass because CX has no agreement (I assume she meant interline agreement) with PQ, but that if I had flown PAL she could have issued a boarding pass.
The end result, I had to enter Hong Kong, proceed to the Departure counters, obtain my boarding pass, go through border control and then proceed to my flight. My question is, where can one find a list of which airlines have interline agreements with CX so that you can be aware when arriving in HKG when you can transfer and when you can not.

ExpertFlyer has such a list. I think you can even do a trial for a few days free.

But PQ is not on CX's list. PR is.

Did this other airline not have their own transfer desk in the transfer desk area before immigration?

It is my personal belief that you have been misinformed, as well as other stuffs.

Don't see why CX can't issue a BP, given flights were booked in separate tickets and no checked baggage was involved.

There's a whole Wiki dedicated to that
https://www.flyertalk.com/forum/cath...gage-faqs.html

Did you not have a mobile phone on which you could have done an online check-in and used the mobile boarding pass?

You are obviously an experienced traveler and what I attempted must be tried by others regularly, yet other posters appear by implication to accept that what happened is unexceptional. Is traveling through HKG and CX such a lottery with regards to staff and rules?

I would say no. It was simply your bad day.

HKG makes it explicit on how transfers are done:

https://www.hongkongairport.com/eng/...rocedures.html

Per your OP, what puzzled me was if the transfer desk can't issue the BP, how the check-in counter can issue the BP. Given no baggage is involved, the transfer desk was simply a check-in counter at the airside.

Without wanting to go on ad nauseam about my little experience even the webpage you referred to above is unclear due to its use of the words "connecting flight" ie connecting from my point of view or from the airline industry's point of view.
I mean I agree with you, surely a transfer desk is merely a check-in counter which does not handle luggage or as you say an airside check in counter. If not then the transfer desks are merely issuing BP's which should have been issued by the initial carrier, ie the interline partner.
But to draw the thread to a close I will follow your advice and treat what happened as an error from the CX staff and maybe if it happens again not give in so quickly.