Two spaceships are moving at relativistic speeds. Due to time dilation the "current time" on one ship is several decades behind the?

There won't be anything equivalent to a lightning bolt to "equalize" the frames. The calendar date will be the same as the date at the dock. The ships will have each measured a different duration, which are both correct, and related to each other by the Lorentz Transformation. There have been experiments conducted using extremely precise atomic clocks in orbit, which compared to the same atomic clocks on the ground, experience different lengths of time, i.e. the whole point of time dilation. If there was some kind of "equalizer", then time dilation would not be observed.

"Two spaceships are moving at relativistic speeds. Due to time dilation the "current time" on one ship is several decades behind the?"

"I've got two spaceships. Both are moving at relativistic speeds. One has been in space a lot longer than the other. Because of time dilation the dates on the two ships are different by several years. The two ships dock."

You have to really careful discussing "dates", since this is deeply embedded in the motions of Earth around the Sun. Theoretically, you can see the Earth moving around the Sun, or have the Earth transmit a time beacon...

"Now when two bodies that have different electrostatic states, lightning occurs and it equalizes the two states."

"Would anything similar occur when the two frames of reference with different dates come into contact?"

Nope. There is no "time potential" to equalize. Each ship is in contact with every instant *now*, they just assign different durations between intervals depending on their relative speed.

The basis is here:
http://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis

And here:
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/experiments.html#Tests_of_Einsteins_two_postulates

We really can't answer this as you've not given us essential information. Like, "relativistic speeds" relative to what reference frame(s)?

If they are moving relative to each other, W, then the time dilation relative to each other is dt = dT sqrt(1 - (w/c)^2). W = (U + V)/(1 + UV/C^2) is the space and time adjusted relative speed between U and V, the two ships. Which means when they dock, their present times will become one present time stream, dT.

If they are moving relative to a designated static reference frame, e.g., Earth, then the dilation is for each, U and V, relative to Earth time dT. Which means when they dock, their merged present times dt will become one dt depending on what speed they dock at relative to Earth.

In either case, the lesson to heed, when one frame joins another, the rates of time become one rate. Which rate, one of the two ships or Earth, depends on the scenario.