Point of contact with a capacitor plate & rolled design?
Performance specifications on Capacitors;


C [pF to F]
Tolerance of C [%]
Vmax [V]
leakage current @ Vmax  [uA]
ripple current [Arms] some temp rise.
dissipation factor ( % of 120Hz power lost for rectifiers)
SRF (self resonant frequency due to inductance)


Joining "a" to "e" are in the same conductor plate and thus have the same E-Field so it is not a variable for capacitance design. 

When the other plate is joined to itself we now have a coaxial capacitor. This is dependent on the gap and dielectric constant to yield some C value in picoFarads per meter.  e.g. coax cable ~ 100 pF/m 
E fields between 2 points decay rapidly with gap will depend on this geometry of equal potential, namely by ;    


1/r³ from a point,    
1/r² from an edge
1/r  from a large area.


Getting to a "tiny centre point " now degrades the contact resistance and with a skinny wire adds inductance.

So this is counter-productive to "performance".  Although the ideal conductor has the same voltage at every point, there is conductor resistance but it still does not affect a constant E field between the plates . 

The Effective Series Resistance, ESR is limited by the area to dielectric total area contact.
This conductor surface may be etched to increase the roughness and effective surface area to thus drop the ESR.

The contact point should be at least the entire edge.