The only part of a phrase which cannot be omitted is ...
... the Head
... the post-Head
... the pre-Head
She quickly opened the letter with trembling fingers contains
a noun phrase with a post-Head prepositional phrase
a post-modified noun phrase
two post-modified noun phrases
a verb phrase with a pre-Head adverb phrase and a post-Head prepositional phrase
The sentence "She finally acceded to his demands for money is best analysed as
a noun-phrase with a post-Head adverb phrase + a verb phrase with a pre-Head adverbial phrase and 2 post-Head prepositional phrases with a noun-phrase complement
a pronoun Head + a verb phrase with a pre-Head adverbial phrase + 2 post-Head noun phrases
a pronoun Head + a verb phrase with a post-Head adverbial phrase and a post-Head prepositional phrase with a noun-phrase complement
a pronoun Head + a verb phrase with a pre-Head adverbial phrase and 2 post-Head prepositional phrases with noun-phrase complements
A prepositional phase usually consists of
the Head preposition plus its noun phrase complement
the Head preposition plus an adverb phrase complement
the Head preposition plus a post-Head verb phrase complement
the pre-modifying pre-Head plus the Head preposition
The subject noun phrase in the sentence "The complex reasons for the disaster which have never been properly analysed have been the subject of much heated and uniformed debate in this House." is
The complex reasons for the disaster which have never been properly analysed "
The reasons
the subject of much heated and uniformed debate in this House.
The complex reasons for the disaster
"Unfortunately for me, nobody spoke any English" contains
a prepositional phrase with a pre-Head modifier
a noun-phrase pre-Head string 'nobody'
an adverb phrase with a post-Head prepositional phrase
a verb phrase with a pre-Head adverb phrase
He worked just over two hours before giving up contains
a pre-modified preposition
a post-modified prepositional phrase
a pre-modified prepositional phrase
a pre-modified verb phrase
We can't say He is fond because
the noun phrase needs a post-Head adjective
it's a transitive verb
the adjective always takes a post-Head
it's an intransitive adjective phrase
Verbs which never take a noun phrase as the post-Head are
ditransitive
intransitive
defective
transitive
In this: The farsighted decision not to build near the river has been a great benefit to the community, we have
a pre-modified verb phrase
an adverb phrase
two noun phrases, both containing a pre-modifying adjective phrase