In the sense of unity of empire as a single political entity, not saying who's righteous or not, the culprit of splitting the empire apart was most certainly Liu Bei aided by Zhuge Liang. The decisive moment was of course the battle for Jingzhou.
It was never known as the Red Cliff Battle during that era. It was known as Red Cliff only after that, when people saw that the cliff was burned charred red and stayed red, even until today if you visit it. Monumental testament to a monumental battle.
Back to Jingzhou, one must have a sense of proportion. It wasn't a mere city. A zhou was the largest district boundary in Xia-Shang-Zhou era, when the whole China comprised nine zhous only. Hence, whole China was called wanfang jiuzhou. In Xia-Shang-Zhou era, every zhou was divided into dukedoms and fiefdoms, hence we had the Spring and Autumn, Warring States periods at the end of the era to sort it out.
In Qin and Han era, the zhous were divided into shires that are further divided into prefectures. What people like Sun Ce tried to do was to restore autonomous lordship over his ancestral land without actually betraying or seceeding from the Han empire. The state of Wu, geographically called Jiangdong (east of River Yangtze) was in the area of Yangzhou. The north from Youzhou to Yongzhou in northwest and Qingzhou in northeast were de facto Cao Cao terrorities and de jure direct imperial terroritories since Cao Cao was Prime Minister representating the Emperor in name for all military and political affairs.
In between was Jingzhou and and west of it was Yizhou (modern Sichuan area). These two are straddled between whether recognising Cao Cao's authority to represent the Emperor or not, as both were held by imperial uncles, Liu Zhang and Liu Biao. To complicate matters of legitimacy, Cao Cao himself became imperial father-in-law too. The Empress was his daughter. Liu Bei (great grandson of Prince Zhongshanjing and in lineage also imperial uncle himself) came in to stake a claim.
Liu Zhang in Yizhou was practically untouchable without taking Jingzhou from Liu Biao first, because of the geography and terrain. In between was what commonly known as Han Zhong (where their ancestor Liu Pang built his kingdom and foundation for Han Dynasty). That's why lands on both sides of this area were conferred to Liu descendants only, never awarded to any non-Liu officials regardless of achievements.
Liu Bei's great grandfather somehow fell out of favour and ended up without land, and Liu Bei, despite from imperial lineage, grew up in relative poverty, or at least austerity. The chaos caused by Zhang Jiao (Yellow Turban rebellion), followed by He Jin, Dong Zhuo and ultimately Cao Cao taking control of a young adolescent Emperor, was what Liu Bei saw as his heaven-given opportunity to reclaim his birthright.
Cao Cao at that time, after taking Jingzhou, with his terroritorial and numerical superiority, would in short eventuality, subdue Sun Quan regardless how clever Zhou Yu was. The automatic surrender from Liu Zhang would follow with the geographical advantage reversed into disadvantage and cornered with Cao Cao controlling Jingzhou and Yangzhou (the land of State of Wu). That's why Zhuge Liang always insisted it must be Jingzhou to take first, losing Jingzhou would be losing the plot.
After the Cao Cao defeat in the Red Cliff Battle, Zhuge Liang immediately occupied the whole of Jingzhou for Liu Bei, much to the distress and anger of Sun Quan and Zhou Yu. Then followed by expedition into Yizhou and finally by half-force half-persuasion, took over the whole Bashu (as it was commonly known then). That was how the State of Shu-Han was established. Liu Bei had prevailed over his better-privileged cousins and became then the top power in Liu imperial lineage.
However, this also created the tripod stalemate that the Three-Kingdom was. Cao Cao would find it very hard to invade Shu without army passing through Jingzhou. Jingzhou was heavily defended anchored by Guan Yu whom Cao Cao had lots of respect for. On the southside, Sun Quan was also trying to figure out how to invade Jingzhou. This problem was solved for him by Lu Xun many years later, when Guan Yu became old and complacent. In any case, he managed only a half-victory (though Guan Yu was captured and executed). The ultimate folly of growing old and more complacent was committed by Liu Bei himself in the Battle of Yiling when Sun Quan scored total victory. Cao Cao and later Cao Pi were no fools too and defended north and central from Zhuge Liang's frequent excursions very well, especially with Sima Yi commanding the defence lines. The whole scenario went back into a stalemate.