My understanding is that gerund is not "zarffiil". But you have a title wth "gerund" and are giving "zarffiil" examples.

I would like to be corrected by an English native speaker who knows the subject very well if my understanding is wrong. Anybody?

Ok. Let´s rename it then..What would your suggestion be Si++ ?

Is there any English grammar term that exactly fits to " Zarf Fiil " ? Or shall we just use Turkish name for it [ Ulaç or Zarf fiil ]?

It seems that our terms are all over the place now. Good. The worse the better.

I will have to dust my old Russian grammar books now because that´s where I met the term for the first time. I have a feeling they support the adverb view...but where does this duality in terminology root from?

I think there is an explanation for it in post #6 (last part).

There is also this in wikipedia page:

In the Molesworth books by Geoffrey Willans and Ronald Searle, Searle included a series of cartoons on the "private life of the gerund"^[3], intended to parody the linguistic snobbery of Latin teachers´ striving after strict grammatical correctness and the difficulty experienced by students in comprehending the construction.

"Converbial Suffixes "  or " Adverbial Suffixes"  are my suggestions.

Followings might help you in your search ;

1-      Деепричастия несоверишенного вида – Sürekli zarf-fiiler

You mean like...the Rolling Stones.

There is a counterpart for the English present participle in Turkish also and the one who has tried to translate relative clauses from E to T or vice versa has noticed that these forms pretty well correspond with each other...

                           Işleyen demir pas tutmaz.

...which is not the case with adverbials of time.

(What...shouldn´t it be işlenen demir?)

After I ve done some research ,I noticed that linguists and Turkologs call it as Gerundium [zarf-fiil]

Prof Dr. Muharrem Ergin and other linguists call them as "Gerundiums" and he says ;

´Gerundiumlar hareket hali ifade eden fiil şekilleridir. Bunlar ne fiil çekimleri gibi şekle, zamana ve şahsa bağlanmış bir hareket, ne de partisipler gibi nesne ifade ederler. Gerundiumlar şahsa ve zamana bağlanmayan mücerret bir hareket hali karşılarlar. Hal ve durum karşılayan kelimelere zarf diyoruz. Şu halde Gerundiumlar fiillerin zarf şekilleridir. a.g.e s.427´

I agree with you, hocam..

Gerund(ium) is zarffiil in Turkish grammar:

Faruk Kadri Demirtaş: "Gerundiumlar, fiillerin zarf şekilleridir.."1 

Muharrem Ergin: " Gerundiumlar hareket hali ifade eden fiil şekilleridir...gerundiuma da zarf fiil diyebiliriz...yani çekimli fiillerin fiil zarflarıdır." 2

Tahsin Banguoğlu: "Zarffiiller (gerundiumlar) fiilin zarf işleyişine girmek üzere aldığı şekillerdir." 3

1 Faruk K. Demirtaş, Eski Türkiye Türkçesi, s. 137.

2 Muharrem Ergin, Türk Dil Bilgisi (11. baskı, s. 338.

3 Tahsin Banguoğlu, Türkçenin Grameri, s. 427.  

After taking a closer look at the concept of gerund I feel like it is another forced exportation of Latin grammar into many languages. Whether its use brings anything useful to a language like Turkish I don’t know.

si++ brought up the definition of English gerund. It’s puzzling. The closest colleague of English gerunds seems to be the verbal noun –mA.

Russian gerunds can be used instead of subclauses. Interestingly, all the examples in my grammar book would be translated into Turkish with the structures tunci introduced in post 1, for example:

Интересуясь русским языком Джон решил изучить его. ’John decided to study Russian language because he was interested in it.’

Написав письмо, я пойду гулять. ’After writing the letter I will go for a walk.’

About Turkish gerunds I would say:

1. They are verb forms or postposition expressions of (often) time. They have various morphological forms.

2. They function as an adverbial in the clause. Maybe this is the most suited definition.

3. Their meaning equals with meanings of gerunds of some languages.

4. What Turkish and English “gerunds” maybe have in common is the ability of the verb form to take further modifiers. Otherwise their connection remains a mystery.

- mIş kadar

When this gerundium suffix comes to  the verb stem , it gives the meaning of "as if"

Sınavdan iyi not alınca, sınıfı geçmiş kadar sevindi.

When he got good point from the exam, he was as much happy as [ if ] he passed the class.

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It was only a good point that he got from the exam, there are still more exams to pass but he felt so happy as if he passed the [whole year] class.