Hi,
The demo board for the MP5061 has 2 capacitors at the output, 10uF and 220uF.
In a system with a cable for power distribution, the end output capacitance may be on a board that is located far away.
What is the minimum output capacitance needed for the MP5061 to behave properly (i.e. no oscillation)?
I would say that 10uF would be the minimum. This part is not a switching regulator. It does not need a lot of capacitance to keep the Vout up due to the discharge cycle seen in switching regulators.
The oscillation will be more dependent on the up and down stream regulators.