C12-3:    Há quem defenda, no entanto, que se trata de um fax apócrifo, realmente escrito por o deputado José Magalhães, o qual teria, aliás, imitado a letra do ex-deputado António Barreto.
 

Before going into the syntax of the verb haver in this particular sentence, it is important to be aware of the forms it takes.  The verb haver has two different semantic forms which interferes with the verb inflection. Haver may semantically mean existir (exist) or it may work just as an auxiliary verb, that can be replaced by ter. Table 1, sums up the semantic form and its implications in the verb inflection:
 

Table 1: Verb haver, semantic form vs. verb inflection
Semantic form
Verb inflection
          Haver= existir        3rd person singular form (unique form, independently of the person, number), 
       varying according to different tenses:
 
    TENSE
 INDICATIVE
SUBJUNCTIVE
               Present Simple                     Há                   Haja
               Past Simple                     Houve                      -
               Imperfect                     Havia                   Houvesse
              "Mais que Perfeito"                     Houvera                      -
               Future Simple                     Haverá                    Houver
          Haver, auxiliary verb ( =ter)        Inflection bearing in mind person, number and tense (all forms present). 
      Always followed by the Past Participle of the main verb or que (in há que fazer)

Let's focus now on the verb haver, meaning existir. Consider the following examples:

(Ex. 1) Houve guerras mundiais no passado, mas agora paz.
(Ex. 2) *Haviam divergências quanto a ideologias entre os países da Europa, o que provocou uma enorme tensão diplomática.
 

In (Ex. 1),  houve, by its non-inflecting characteristics (houve: 3rd person singular; guerras: noun , feminine, plural), stands for existir. Even though the replacement by the verb existir is possible,  inflection occurs, which is explained below by the syntactic differences between the constructions with haver and existir, respectively:

(Ex. 1') Existiam muitas guerras mundiais no passado, mas agora existe paz.

On the other hand, (Ex. 2) is not acceptable when the existir meaning of haver is concerned, as the verb presents inflection in person and number.  Haver, therefore, would be expected to be followed by the past participle of a main verb (Ex. 2')

(Ex. 2') Os países da Europa haviam divergido quanto a ideologias, o que provocou uma enorme tensão diplomática.

Here, the auxiliary verb replacement by existir is, then, innacurate (Ex. 2''), but works for ter (Ex. 2'''):

(Ex. 2'') *Os países da Europa existiam divergido quanto a ideologias, o que provocou uma enorme tensão diplomática.
(Ex. 2''')  Os países da Europa tinham divergido quanto a ideologias, o que provocou uma enorme tensão diplomática.

Applying these considerations to the initial sentence (C12-3), quem defenda, no entanto, que se trata de um fax apócrifo,......, and realising that the verb haver is not followed by the past participle of another verb, it must stand for the semantic meaning of existir:

(S1) Existe quem defenda, no entanto, que se trata de um fax apócrifo, realmente escrito por o deputado José Magalhães, o qual teria, aliás, imitado a letra do  ex-deputado António Barreto.

Moving to the syntactic analysis, existe is the finite main verb, and the subject is the whole period "quem defenda, no entanto, que se trata de um fax apócrifo, ". However, the semantic substitution cannot be applied to the syntactic substitution. In other words,  the verb existir is intransitive, therefore, "quem defenda, no entanto, que se trata de um fax apócrifo, realmente escrito por o deputado José Magalhães, o qual teria, aliás, imitado a letra do ex-deputado António Barreto." has to be the subject.
The same is not true for haver. The verb is transitive, so it requires a direct object, but there is no subject in this type of construction (haver= existir).

A1
STA:fcl
P:v-fin(PR 3S IND) Há
ACC:fcl
=SUBJ:pron-indp(<rel> M/F S/P) quem
=P:v-fin(PR 3S SUBJ) defenda
=,
=ADVL:adv(<kc>) no_entanto
=,
=ACC:fcl
==SUB:conj-s que
==ACC:pron-pers(<refl> M/F 3S/P ACC) se
==P:v-fin(PR 3S IND) trata
==PIV:pp
===H:prp de
===P<:np
====>N:art(<arti> M S) um
====H:n(M S) fax
====N<:adj(M S) apócrifo
==,
==>A:adv realmente
==N<PRED:icl(<pcp>)
===P:v-pcp(<ap> M S) escrito
===PASS:pp(<postmod>)
====H:prp(<sam->) por
====P<:np
=====>N:art(<-sam> M S) o
=====H:n(M S) deputado
=====N<:prop(M S) José_Magalhães
=====,
=====N<PRED:fcl
==SUBJ:pron-indp(<rel> M S) o_qual
==P:vp-
===AUX:v-fin(COND 3S) teria
==,
==ADVL:adv(<kc>) aliás
==,
==-P:vp
===MV:v-pcp(M S) imitado
==ACC:np
===>N:art(F S) a
===H:n(F S) letra
===N<:pp
====H:prp(<sam->) de
====P<:np
=====>N:art(<-sam> M S) o
=====H:n(M S) ex-deputado
=====N<:prop(M S) António_Barreto
.

In other constructions, haver as an auxiliary (= ter), does possess a subject, because it is the main verb that governs the valency, not the auxiliary. In (Ex. 2'),

(Ex. 2') Os países da Europa haviam divergido quanto a ideologias, o que provocou uma enorme tensão diplomática    ,

 the subject  is the noun phrase, "Os países da Europa". The sentence does not present a direct object because the main verb divergir is not a transitive verb.  Here's another example where the main verb is transitive:

                a) Os países haviam quebrado o princípio básico da diplomacia.

         SUBJ:np ----   Os países
         FAUX      ----   haviam
         FMV       ----   quebrado
         ACC:np   ----   o princípio básico da diplomacia
 

A good test to check the valency of the verb haver, meaning existir, is the pronoun substitution test (PS) . The direct object would allow the replacement by a pronoun:

(Ex. 1) Houve guerras mundiais no passado, mas agora paz.
 PS:    Houve-as no passado, mas agora há-a.                        (as, standing for guerras mundiais;  a, standing for paz)

C12-3: Há quem defenda, no entanto, que se trata de um fax apócrifo, realmente escrito por o deputado José Magalhães, o qual teria, aliás, imitado a letra do ex-deputado António Barreto.
PS:       Há-os.            (os, standing for  "quem defenda, no entanto, que se trata de um fax apócrifo, realmente escrito por o
                                       deputado José Magalhães, o qual teria, aliás, imitado a letra do ex-deputado António Barreto.")
 

The lack of inflection itself, meaning no subject-verb agreement, might also indicate that there is no subject when haver semantically means existir.
Other examples in the sentence corpus:  C5-10

There are other constructions with the verb haver, where, despite the fact that it does not mean existir semantically, it is also impersonal (no subject) and it takes just a unique form (3rd person singular). That's the case when haver stands for time duration. See examples and discussion in haver_time.