Does there exist a single plate capacitor(conductor)? Does there exist a single plate capacitor(conductor)? if yes
How will you define the capacitance and potential(difference)
of such conductor?
 A: A simple example is that of a sphere. One way to find its capacitance is to take the limit of a nested sphere capacitor with radii $a,b$:
$$C = \lim_{b\to\infty}\frac{4\pi\epsilon_0}{\frac{1}{a}-\frac{1}{b}} = 4\pi a\epsilon_0\text{.}$$
A van de Graaff generator is a commonly discussed in physics classes, and involves this type of setup.
For a parallel-plate capacitor, however, doing the same gives zero capacitance.
A: A single conductor also possess capacity to store charge. It may be treated as parallel plate capacitor, whose one plate is at infinity. 
If this doesn't help, comment on the part where you have problem.
A: Yes. Capacitance is very well defined for a sphere in vacuum,  and can be extended to other media and shapes. The following is a simple abd correct  definition of capacitance. Adding other conductors disturb the capacitance of a single conducting body,  giving rise to mutual capacitance. 
The following is exerpted and edited from The Great Soviet Encyclopedia (1979). Search that term for more complete answer. 
Capacitance 
The capacitance C of an isolated conductor is equal to the ratio of the charge on the conductor to the conductor’s potential. 
Capacitance is determined by the size and shape of a conductor and by the electrical properties of the surrounding medium, that is, by the medium’s dielectric constant. Capacitance of a conducting sphere in vacuo is equal to the radius of the sphere. Capacitance is measured in centimeters in the cgs system and in farads (1 farad = 9 × 10^11 cm) in the International System of Units (SI).
