Nick wrote:

If I have it right, they are also known as West African limes, and
the Americans know them as Mexican ones :-) God alone knows where
they originated! They are the usually the ones bought in the UK,
and the plant is definitely a tropical one - i.e. it needs fairly
constant warmth and high humidity.

I was a bit wooly-headed when I rattled off my earlier comments and on
re-reading, see that I got the bit about thickness of rind back to
front. The 'Tahiti'/'Persian' lime has the thicker rind. Sorry about
that - was just waking up - dyslexic thinking ;-)

West Indian limes Nick a.k.a. Key lime, Mexican Key lime, bartender's
lime etc. etc. They may be grown in West Africa and therefore may be
dubbed that by some. It is thought to have originated in the Far East
and was brought to the Middle East by traders at some point in distant
history. From there it was taken to the New World by the Spanish and
Portuguese. The problem is that there are several Citrus referred to
as limes and since few sellers make any great distinction, the
confusion continues. I am fairly positive that you are referring to
'Key lime', which seems to be prevalent in many shops due to its
prolific nature and flavour.

I haven't often seen these in the UK. I believe that 'Bearss' is a
seedless variety that dominate the USA,

Bearss. is a seedless or near seedless form of the Tahiti/Persian
lime. As you mention, it is primarily sold in the US and is rarely
available here. The similar fruits of the Tahiti lime do make an
appearance - IIRC during early autumn for a month or so.

What is their flavour like and how aromatic is their juice?

Assuming you mean the 'Tahiti', the fruit is less acid and if ripened
in heat (ie a hot greenhouse/climate) it can become almost too sweet
for a lime. It is not as aromatic as the Key lime and is considered
to be a hybrid with Key lime (Citrus aurantiifolia) as one of the
parents and maybe one of the lemons as the other. I understand it was
first developed in the Middle East (hence 'Persian') and was moved
about during the 20th. century.

Which reminds me, I'm doing a fiery chilli for dinner. I'd better
pick a handful of limequats from the bush outside to go with it. Now
they are excellent substitutes for Key limes provided they are not too
ripe and they don't need the heat either - I've been picking them
throughout the winter. Unfortunately they are small, but at least you
get lots of them. You ought to try one in your greenhouse Nick. It is
the Eustis limonella - very easy, cold tolerant and utterly reliable
even as a small plant.