Are sufi schools equally divided amongst the two major branches of Islam - Shia & Sunni, or are they primarily associated with Shia Islam?
Actually the famous Sufi groups and organizations are Sunni not Shia. There is a sensitivity and negative attitude towards them among other Sunni Muslims like some followers of Salafi movement for various reasons that I will not go into in this answer, still Sufi orders have developed mainly among Sunni not Shia.
As far as I know, among mainstream Shia Muslims we don't have similar Sufi organizations and Tarighats. Thoughts similar to Sufi thoughts exist among Shia Muslims. However, it has not turned into similar organizations partly because of the role and the importance of fiqh for Shia. There are famous Shia scholars who practice what is called irfan but all famous ones that I am know of consider only paths within the confines of Islamic Sharia and focuses mostly on how to better perform Sharia. I haven't heard them being referred to as Sufi, the common word to refer to them is Aaref. One of Irfan's main point is the perspective that the laws in Sharia are not goals in themselves but are means to walk towards and get closer to God and obtain light (still there are other Shia scholars who find such thoughts even within the confines of Islamic Sharia problematic).
As far as I understand, in the view of these Shia Aarefs, each person should walk on a path (طریقة) towards God and obtain light (as stated several times in Quran, search for words like walking, path, light, etc., e.g. see verses 1:6, 57:9, 57:12-14, 57:28, 14:1, 6:122) but the best way to walk towards God is following the Sharia (شریعة). In fact, Sharia has a similar meaning to Tarighat: شارع is from root شرع which means street in Arabic.
I think a major point of irfan is to remind one that simply following the appearance of Islamic Sharia is not enough if it does not lead one to obtaining light and walking towards God. If you are performing a part of Islamic Sharia and it is not bringing you closer to God then you are not performing it as it should be performed, e.g. people who think they are praying correctly and according to Sharia but during the prayer their thoughts are not with God but somewhere else, or they performs prayers but also do shameful acts, that means the person is not really upholding prayer, since according to Quran upholding prayer should restrain one from committing sins (see verse 29:45).
Here is an analogy I have heard about their perspective and found useful: if the other paths suggested by Sufi Tarighats are fine and makes one closer to God (which is debatable) Sharia is like a high way compared to them which can take one much faster toward God.
This is to the best of my knowledge, if there is an inaccuracy or problem with the answer I would be happy to hear about it.
Sufism is more of a denominator for a specific approach to Islam. This approach can be found in the teachings of Sunni as well as Shia. Check the site of the Halal Monk for conversations with different spiritual leaders and artists of the Muslim world. Some of them are rooted in the Sufi tradition but sometimes they're Sunni, sometimes they're Shia.
You should remember that your affiliation to one of the four mazhaabs makes you a sunni. But their name is normally known as ahlul sunna wal jama at. If the sufis have any affiliation to one of those mazahibs that means they are sunnis.
It should be noted that Islam gives emphasis to only ibada noting else.
To be a sunni or a shite does not qualify you to get into paradise direct except with iman and ibada.
please brothers and sisters shism and sunnism are all ideologies .the most important thing is ibada.
I myself speaking i am affiliated to maliki ideology but i know shites are also Muslims. Only that they have some wrong ideology.so the difference between us should not cause any trouble .
every one should face himself and do his ibada accordingly.
Nearly all Sufi schools trace their ancestry to Imam Ali a.s., as their genetic father by their masters or as their master in teachings through the holy 12 Imams, most Sufi schools are therefore Shia, but the biggest Sufi school is a Sunni school (Naks-i Bendiyye), but also started as a Shia school of teachings. Therefore they trace their ancestry to Imam Ali a.s., but some claim also ancestry to Ebu Bekir.
Here is a ancestry-line of a worldwide well-known Islamic master: Seyyid Abdülkadir Geylani (k.s.a):
- Hz. Muhammed Mustafa (S.A.V.) (--- through his daughter Fatima a.s. ---)
*2. Hz. Ali (R.A.) [IMAM ALI] *
Hz.Hüseyin (R.A.), Hasan-ı Basri(R.A.)
Zeynel Abidin (R.A.), Habibul Acemi(K.S.A.)
Muhammed Bakır (.R.A.), Şeyh Davud-u Tai(K.S.)
Cafer-i Sadık (R.A.) Maruf-u Kerhi(K.S.)
Sırrı Sakati (KS.)
Ebu Bekir Şibli(K.S.)
Abdulaziz et Temimi(K.S.)
Ebul Ferec Yusuf et Tarsusi(K.S.)
Ebul Hasan Aliyyübnü Muhammed b.el Kureyşli(K.S.)
Ebu Said el Manzumi(K.S.)
Seyyid Abdülkadir-i Geylani(K.S.)
No no brother, Sufism is something that's related with Islam, Shia Sunni Wahabi they are nothing to deal with this. In fact the sufis never relate themselves as being a Sunni or Shia. They love their creator and work for him. They preach the religion, write poems and help people. They have nothing to do with this.
The Shia, are the main decendants of Holy Prophet; Sayyeds. That's why you might be asking this. But no! Sufi schools are not related to any of this system.