There is a famous multicentury argument in the history of Chinese Buddhism as to if enlightenment is something achieved after gradual practice and improvement or something you realize or achieve in a flash of inspiration.
Which schools were gradualists? Was this an actual distinction or was this a rhetorical device? Are there any surviving (as in existing right now) gradualist schools? Was Tien Tai/Tendai/Nichiren Buddhism gradualist?
I'm not a scholar of Chinese Buddhism, all I known is that the gradual enlightenment tradition was referred to as "The Northern School of Chan" and the sudden enlightenment got known as "The Southern School of Chan". Googling for these two terms turns up some useful references. Let's see what we can learn from these...
Wikipedia articles on Chan Buddhism - Southern School, East Mountain Dharma Gate, Subitism - Chan, and Shenhui provide some historical information about the two approaches.
From all the evidence it looks like the distinction was made up and promulgated by Shenhui, the student of Huineng whose adversary Shenxiu was later portrayed as that infamous monk in the Platform Sutra who lost the famous verse contest for their common teacher Hongren of East Mountain Dharma Gate (the original Chan school tracing back to Bodhidharma himself).
Shenhui sharply criticized Shenxiu's Northern School's emphasis on ceremony and sutra study - and contrasted it with seated meditation of Huineng and the original East Mountain Dharma Gate:
Shenhui traveled north to live amongst his ideological enemies in the capital city of Luoyang. While in the city he spoke publicly against the teachings of the Northern School:
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"[Northern School teachings] are the methods of the ignorant. ... In the six generations that have come before [!!! - AV], not a single person performed the practices of Shenxiu."
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This was a polemical exaggeration, since both schools were derived from the same tradition [of Bodhidharma, Daoxin, and Hongren - AV], and the so-called Southern School [the Shenhui's sect - AV] incorporated many teachings of the more influential Northern School [which was a direct descendant of the original Chan! - AV]. Eventually both schools died out, but the influence of Shenhui was so immense that all later Chan schools traced their origin to [Shenhui's teacher - AV] Huineng, and "sudden enlightenment" became a standard doctrine of Chan.
So it looks like it was a rhetorical device coined by Shenhui and popularized by the later Chan tradition to make a case for their "Meditation leading to A-ha Realization" method as an antipode to mere "ceremony and sutra study" which they felt was a degradation of Dharma.
From this standpoint I suppose we could say that any school that does not have a notion of Aha Realization could be considered a gradualist school.
Apparently the gradual approach traces its origins to Yogachara and even further back to Shurangama Sutra and Lankavatara Sutra (According to Traleg Kyabgon Rinpoche, "The Surangama Sutra and the Lankavatara Sutra were the inspiration for Asanga and Vasubandhu to build their system of philosophy.") - while the sudden approach goes back to the prajna-paramita family of sutras.
From this I guess we could infer that those schools that taught Lankavatara and/or Shurangama sutras exclusively were probably the gradualist schools you are looking for.
Late Chan schools should be excluded by definition. It does look like the early East Mountain Dharma Gate was not gradualist either:
[Daoxin, the founder of East Mountain Dharma Gate, advocated for] the unification of the teachings of the Lankavatara Sutra with those of the prajnaparamita sutras [family], which includes the well-known Heart and Diamond sutras.
One Chan school that stands apart is Caodong, the Chinese predecessor of Soto. Apparently it's a school that emphasizes silent illumination (through sitting meditation) without any end result whatsoever. There is simply "no goal to be attained beyond the practice itself." This makes this school neither gradualist nor subitist.
Before Bodhidharma and Chan, the Hua-yen school taught Avatamsaka Sutra, which apparently "integrates the teachings on śūnyatā and Yogacara thinking" - shunyata being an element of sudden realization. Before that, Tiantai school included Avatamsaka Sutra in its "classification of teachings" scheme, and mentioned "Gradual Teaching, for those with medium or inferior abilities vs Sudden Teaching for those with superior abilities". So Hua-yen and Tiantai are not gradualist in the strict sense of the word - although we can't call them subitist either.
The only remaining Chinese schools that I know of are Tangmi (tantric), Faxiang (yogacara), and Pure Land.
Looks like Tangmi did teach Surangama Sutra - and its Wikipedia article says:
In Chinese Buddhism there was no major distinction between exoteric and esoteric practices and the Northern School of Chan even became known for its esoteric practices of dhāraṇīs and mantras.
Faxiang reportedly studied the Heart Sutra among other texts, which would put it into the "integrationist" camp in my book, along with Tientai and Hua-yen. As for the Pure Land, they say unlike in Japan in China it was never a distinct school but rather a tradition permeating other schools - including Chan.
To summarize, it looks like the only school that we can definitely call gradualist was Tangmi, the Chinese precursor of Shingon. If we were to grade schools from completely gradualist to integrative to subitist, Pure Land and Tangmi would be on the far left, then the integrationist schools like Faxiang, Tiantai and Hua-yen in the middle, followed by the early Chan (the first 5 generations from Bodhidharma to Hongren), followed by the late Chan, and finally Linji (Rinzai in Japan) on the far right with its kicking, yelling and koans. I'm not sure where to place Caodong and Soto Zen though - they could either go to the far left if we consider them "infinitely gradual" or somewhere near the middle if we assume their "the path is the goal" to be a clever upaya designed to help the student attain the non-attainment.
Alas for simple theories but this was fun. I learned a lot while working on this answer, so thank you for an interesting question.
