The minimum and maximum amount of plasmid DNA that can be used for transformation of bacteria can vary depending on a number of factors, including the bacterial strain, the size and copy number of the plasmid, and the transformation method being used.
In general, for chemical transformation methods, the minimum amount of plasmid DNA required for successful transformation is usually in the range of 1-10 ng. However, the optimal amount of DNA can vary depending on the bacterial strain and the plasmid being used.
The maximum amount of plasmid DNA that can be used for transformation is generally limited by the capacity of the bacterial cells to take up and incorporate the DNA. Too much DNA can lead to inefficient transformation or even cell death. In practice, the maximum amount of DNA used for transformation is usually in the range of 100-500 ng per transformation.
It is important to optimize the amount of DNA used for transformation in order to achieve the highest transformation efficiency while minimizing any negative effects on the bacterial cells.
In order to answer your question, some terms need to be better defined. First you need to specify what volume of cells in your transformation. For a typically transformation of 100ul of competent cells is not going to give the same answer as a scaled up transformation with more cells. Also what is your criteria for transformation?
Assuming a normal amount of competent cells, what you would see is a curve if you plot transformants per amount of DNA used starting from the lowest amount tested, until you hit the saturation plateau. The minimum will be 1 molecule, the probability of transformation is low but not zero. Even at sub-ng amounts of DNA you will still get lots of transformants.
Saturation is hit probably in the 10-50 ng of typical cloning plasmid and adding more DNA is likely to only slightly increase number of transformants above this. But this isn't really a maximum, just approaching it. At some point though you may start getting into inhibition with even higher levels of DNA.