Nearly all of them admit empty domicile is quite humble (6)
I believe the answer is:
modest
'humble' is the definition.
(associated in meaning)
'nearly all of them admit' is the wordplay.
'nearly all' becomes 'most' (I've seen this in another clue).
'of them' becomes 'de' (I can't justify this - if you can you should believe this answer much more).
'admit' indicates putting letters inside.
'most' enclosing 'de' is 'MODEST'.
'empty domicile is quite' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for modest that I've seen before include "Having a humble opinion of oneself" , "self-effacing" , "Not vain, rather shy" , "Native of Vienna" , "Not having or showing pride" .)