H connects "how" to "much" or "many". "Much" and "many" can serve as determiners ("How many books do you have"); they can also serve as independent noun-phrases ("How many do you have"). Unlike most determiners, they can also be preceded by the word "how" in either case, creating a question or indirect question:
+--H-+-Dmc-+
| | |
How many books do you have
Therefore they have H- connectors, optionally conjoined with
their D+ connectors and also with their main noun
complexes. However: when the H- is being used on "many" and
"much", a question situation is created (direct or
indirect). This introduces constraints on word-order, mainly
relating to subject-verb inversion. For this reason, H+ on
"how" is conjoined with QI-
(used in indirect questions) or
Wq- or Ws-
(used in direct questions). These connectors trigger
post-processing rules; see SI.
H is also in a
post-processing category along with D##w, relating also to
s-v inversion; see "SI:
Questions without s-v inversion".