Question: Which territory did Roman von Ungern-Sternberg's forces and the Transbaikal fight over? 

Context articles: Transbaikal Military District
36th Rifle Division (Soviet Union)
5th Pri-Amur Corps
41st Army (Russia)
Gongota Agreement of 1920
Roman von Ungern-Sternberg
16th Army (Soviet Union)
23rd Air Army
Jalkhanz Khutagt Sodnomyn Damdinbazar
Alexander von Ungern-Sternberg

The Transbaikal Military District (Russian: Забайкальский военный округ ) was a military district of first the Soviet Armed Forces and then the Armed Forces of the Russian Federation, formed on May 17, 1935 and included the Buryat Republic, Chita Oblast, and Yakutia.
 Chita was the headquarters of the district.
 It was finally disbanded on December 1, 1998 by being amalgamated with the Siberian Military District, though Chita remained the headquarters of the new amalgamated district.
The division was first formed as the 36th Rifle Division (ru: 36-я стрелковая дивизия) based on the 9th Army's expeditionary division on 19 July 1919.
 It fought in the Russian Civil War and was part of the 9th Army between 1919 and 1920.
 In summer 1921, the division participated in the campaign against Roman von Ungern-Sternberg's forces in Mongolia.
 On 4 June 1923, the division was given the honorary designation "Transbaikal".
The 5th Pri-Amur Corps (Russian: 5-й Приамурский корпус ) was a formation of the Siberian Army, part of the anti-Bolshevik White movement during the Russian Civil War.
 It primarily operated in the Transbaikal region and was headquartered in the city of Chita.
 The 5th Corps was formed from the Transbaikal Cossacks and various other volunteer forces fighting under "Ataman" (chief) Grigory Semyonov, as part of his Special Manchurian Unit (Особый маньчжурский отряд, OMO).
The 41st Army (Russian: 41-я армия ) is a field army of the Russian Ground Forces, currently part of the Central Military District.
 Originally, it was formed in 1942 as part of the Soviet Red Army, during World War II.
 It was reformed in 1998, when the Transbaikal Military District and Siberian Military District were amalgamated.
The Gongota Agreement of 1920 (Russian: Гонготское соглашение , Japanese: 緩衝国建設覚書 (lit.
 Memorandum of establishing buffer state)) was a milestone in the Russian Civil War in Transbaikal.
 The Agreement was finalized at Gongota railway station on July 15, 1920 between the Far Eastern Republic's delegation headed by Alexander Krasnoshchyokov and Genrich Eiche and the Japanese Expeditionary Corps under Yui Mitsue.
 The Far Eastern Republic's demands were the evacuation of White Army troops from the zone held by the Japanese forces and the end of hostilities between the Soviets and Japan.
Baron Roman Nicolaus Maximilian von Ungern-Sternberg (Russian: Барон Ро́берт-Ни́колай-Максими́лиан Рома́н Фёдорович фон У́нгерн-Ште́рнберг ) (10 January 1886 NS – 15 September 1921) was an anti-Bolshevik lieutenant general in the Russian Civil War and then an independent warlord whose Asiatic Cavalry Division wrested control of Mongolia from the Republic of China in 1921 after its occupation.
 He was often referred to as Baron Ungern, or simply Ungern.
The 16th Army Headquarters was formed in July 1940 in the Transbaikal Military District to command Soviet forces deployed in the Dauriya area.
 On 25 May 1941, four weeks before the commencement of the German invasion of the Soviet Union, Operation Barbarossa, the army received orders to deploy (with six Trans-Baikalian divisions) to the Ukraine to be subordinated to the Kiev Special Military District.
 The first 16th Army units to arrive (109th Motorized Division of the 5th Mechanized Corps) in Berdichev on 18 June 1941.
 The Army was commanded by Lieutenant-General М.
 F. Lukin, and on 22 June the Army Headquarters was located in Orel.
The 23rd Air Army was an Air army of the Soviet Air Forces and the Russian Air Forces, active from the 1960s to the 1990s.
 It traced its origins to the 12th Air Army, formed during World War II, and served in the Transbaikal region for the entirety of its career.
The Jalkhanz Khutagt Sodnomyn Damdinbazar (Mongolian: Жалханз Хутагт Содномын Дамдинбазар ; 1874–1923) was a high Buddhist incarnation from northwestern Mongolia who played a prominent role in the country's independence movement in 1911-1912.
 He served as Prime Minister twice; first in 1921 as part of the Bogd Khan puppet government established by Roman von Ungern-Sternberg, and again from 1922 to 1923 under the revolutionary government of the Mongolian People's Party.
Peter Alexander Freiherr von Ungern-Sternberg (22 April 1806 – 24 August 1869) also known as Alexander von Sternberg, was a Baltic German novelist, poet and painter who worked under the pseudonym Sylvan.