How Do Amps Affect Soundstage?

In my admittedly limited experience, amplifier soundstaging is most affected by channel separation/crosstalk (hence, all else being equal mono blocks better than true dual mono better than stereo), sufficient real power (voltage and current), and competent design. For a moderate power and price amplifier, see Stereophile and Audio Science Review test results of the Benchmark AHB2.

The more info I have the better thanks

Amplifiers matter because of noise, white noise accumulated through signal conditioning and amplification stages. Dead quiet to loud matters. Tubes, like jfets, and mosfets do not have a lot of current input and therefore have almost zero current noise. Voltage noise can be mitigated relatively easily. The listening  experience that enlightened me is from a Counterpoint Solid 2, blown up, that I fixed and changed minutely to drive, any speaker or simply weld to music. I was completely blown away after getting it going.. I wanted to listen to this thing, testing forever with my elac 6.2 debut monitors. My friend Dave, the amps owner was blown away too. Preamps because of noise, and of course speakers the biggest deal.      

Nelson Pass uses a technique of adding an out of phase 2nd harmonic distortion to his designs. This will give you more spatial information and the feeling that the notes are in the air. 

If we think about it in it’s simplist terms, a deep, wide soundstage requires a stereo signal. The more "mono" the signal is, the more it will "move to the center" narrowing the soundstage assuming the channels are in phase.  If the channel interactions are out of phase, the soundstage gets more "nebulous" as separation is lost.

So, it would seem that an amp that has poor channel separation would not produce as nice and wide a soundstage as an amp that has better separation. And of course, anything (e.g., interchannel distortion) that affects both channels similarly is also in mono so hurts the soundstage presentation.