J connects prepositions to their objects.
+-Mp+----J---+ +-----MVp----+-J-+
| | | | | |
The man with the hat chased the dog on Tuesday
Proper and common nouns, accusative pronouns, and other words
that can act as noun-phrases have "J-" disjoined with their
S+, SI-, and O- connectors.
Prepositions have "J+ & (Mp- or MVp-)". "Mp" is used for prepositions modifying nouns; "MVp" is used for prepositions modifying verbs and adjectives. Prepositions may also have other connectors, disjoined with J+, such as Mg+, Mv+, and QI+; see "MV: Other Uses of MVp and MVs".
+----------Op---------+
| +----Dmc----+
| +--Ds-+-OFd-+--Jd-+
| | | | |
I.p have.v a number.d of cookies.n
In the above example "a number of" is acting effectively as
a determiner phrase. Thus, its head word, "number", gets a D+
link. Yet, the phrase ends with a preposition that shouldn't dangle,
and so, for this case, a Jd+ link is also used to complete
the loop. Plural and mass nouns have a
(Jd- & D- & O-) disjunct on them.