The TransBaikal Host was based on the area east of lake Baikal, with their lands around the border area, but politically centred on Chita. The Ataman of the host was historically commander of all Imperial troops in the area. Its soldiers wore standard Cossack dress, with their distinguishing colour being yellow.
TransBaikalia was utterly dominated throughout the Civil War period by one man: Grigorii Semënov. He set up the first serious anti-Bolshevik forces in Siberia, and was fighting when others were merely blustering or still plotting underground.
Grouping a few reactionary officers, some locals and foreigners fleeing the Reds, he raised his Special Manchurian Detachment, the OMO (named after the town of Manzhouli, not the province of Manchuria) across the border in China. He was able to persuade the Japanese to support him with both money and arms. He then made a serious attempt to take TransBaikalia in early 1918. With few other military threats at that time, the Soviets were able to concentrate all their Siberian forces against the OMO, and Semënov was pushed back nearly into China.
However, when the Czechs started the clear their path to the east the OMO already had substantial forces and was able to take advantage of the new threat to the Soviet rear. In June 1918 Semënov already had about 5,000 men, and he and Czechs cleared the Trans-Baikal region of all formal Red forces from July to September.
While he was a Cossack himself, local Cossacks were reluctant to join his forces. Instead the OMO was largely Buryat Mongols and Chinese, commanded by Russians and foreigners. There was also a small, but militarily significant, Japanese contingent from the start. The OMO also already had a couple of the armoured trains that were to dominate the fighting in the east, plus at least one armoured car.
Once in power Semënov instituted a reactionary regime, intended to benefit himself and his immediate supporters rather than further the White cause. Incapable of building on the anti-Soviet feeling that Siberians generally felt, Semënov proved to be every bit as bad. The TransBaikal Cossacks were no more impressed than anyone else, and while regiments appeared on the payroll, troops failed to turn up to fill them. Instead Semënov drafted in more Buryat and Tungus tribesmen and any foreigners trying to head east – ending up with a substantial Serbian unit, for example.
Anti-Semënov partisan strength grew tremendously in 1919, as it became clear that Semënov's forces could not defeat them. The Japanese able to keep him in power, but not suppress the partisans. The atrocities of the OMO and their Japanese allies further stoked discontent, leading to mutinies and revolts. In July 1919 the 1st TransBaikal Semënov Regiment killed their officers and went over to the Reds. By now partisan attacks were full scale assaults on towns, not just isolated attacks on easy targets. From a heady mix of anarchists, SRs, refugees and bandits, they were increasingly infiltrated by Bolsheviks, who provided the organisation and cooperation that was otherwise lacking.
By the end of 1919 the Red Army was on the borders of TransBaikalia, Irkutsk having fallen to Red partisans just ahead of the advancing Red Army. Semënov's forces were now the front line, and the only force not actively retreating. As a result in January 1920 the Ataman was proclaimed Supreme Russian Authority, that is commander of the White movement, despite his unpopularity with White supporters.
The remnants of Kolchak's White Army, the kappel'evtsy, struggled into TransBaikal at the start of 1920. There they received food and shelter, but more importantly they lost their pursuers. The regular Red Army did not want to fight the Japanese, for diplomatic reasons, which limited their military options (though the partisans continued to fight anyone). Also the nationalist units of Czechs, Romanians and Poles were now often the rearguard of retreating forces, which forced them back into active combat with Soviet forces: something they had been avoiding for the previous year. It took a long time for the Red Army to mop up these forces and consolidate its position in western Siberia.
When the kappel'evtsy arrived in Chita in March 1920 they were commanded by General Voitsekhovskii, Kappel' having fallen to frostbite in early 1920. Despite their intense loathing of Semënov, they realised that they would have to work with him to survive. They reorganised into the Far Eastern Army, but were soon pinned to a small strip along the Trans-Siberian railway.
Technically White forces were now opposed by the Far Eastern Republic, which was Lenin's puppet regime east of Lake Baikal. The Soviets did not want to be seen to be officially fighting Japan, but wished to do so via the FER's "People's Revolutionary Army", the NRA. In fact the Red Army continued to send units east of this line from time to time, as the division between Soviet Russia and the FER was entirely arbitrary.
In April the NRA attempted to take Chita, which would have removed all significant White forces from Siberia. They were opposed by the Japanese, the kappel'evtsy and the OMO. The TransBaikal Cossacks, with their homeland in desperate straits, were now finally fighting for the White cause in decent numbers. This motley collection held out until October. In August Semënov's assembled forces were up to 20,000 men, nine armoured trains and 175 guns.
By November 1920 the remaining White forces had been pushed back to the Chinese border near Manzhouli. They attempted to get permission from the Chinese to cross via the railway to Primorye still armed, but in the end they had to agree to surrender their weapons as they crossed the border.
Many opted to cross over to Primorye, where the last White stand on Russian soil would be made. A TransBaikal Cossack Divizion was included in those forces, although Semënov himself was not welcome.
The Special Manchurian Detachment was a polyglot mixture, with frequent changes in its order of battle and a confusing history. It wasn't really a particularly Cossack army, although the Buryats and Tungus were probably dressed in more or less Cossack uniforms for want of anything better.
Supply was largely Japanese, although large amounts of British and US equipment were pilfered from the Trans-Siberian on their way to Kolchak.
Jamie Bisher, "White Terror: Cossack Warlords on the Trans-Siberian", is far and away the best source in English for anyone trying to follow the military history of the OMO or assemble orders of battle.