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No, they were generally led by the guards from the prison camps.
The killing units were part of his Final Solution and dream of a pure Aryan European world controlled by him. He eliminated a lot of undesirables with his mobile killing units.
By "mobile killing units" I am assuming you are referring to the einsatzgruppen. They were disbanded because they were inefficient, expensive, and they had a difficult job that was having a negative effect on their morale.
There were mobile killing units (SD-Einsatzgruppen) which went into action behind German lines in the Soviet Union.
they were told where to go and how many people they had to deal with to perform their task
They were called Einsatgruppen (or SD-Einsatgruppen). In English they are often referred to as mobile killing units.
The Einsatzgruppen were mobile killing units (death squads) that operated behind German lines on the Eastern Front. They were under the control of the SD, which was headed by Heydrich till his assassination in June 1942. Their main function was exterminating Jews. (Other units were used against guerrillas).
The special units to kill the Jews were the Einsatzgruppen (often referred to in English as 'mobile killing units').
These groups are called "Einsatzgruppen" and would round up Jews and shoot them to death. The project was replaced with the death camps in order to preserve the bullets.
In the extermination camps the victims were gassed, then cremated. When killing 'in the field' the mobile killing units sometimes herded Jews into buildings which were then set on fire.
The genocide began in June 1941 as the mobile killing units went into action behind German lines in the then Soviet Union.
The Soviet Union
They followed some miles behind the front line looking for those types of people who were seen as a threat to security.