Minimum space between square taper crank and bottom bracket I upgraded to a new square taper crankset on a single-speed drivetrain and now the gap between my crank and the bottom bracket is bigger. That's because the cranks taper shape is different from the one I had before and I haven't changed the bottom bracket. This (along with a different shape of the crank) made the Q-factor bigger. I wanted to reduce it, so I ordered a new bottom bracket with a shorter spindle. I checked the measurement already and it's going to be all good with chainstay clearance. The question is:

How close can a square taper crank be to the bottom bracket? How small can the gap in the picture be?
You can reduce the gap between the crank and frame to essentially zero as long as the crank does not rub in the frame. However, that is not really how square taper cranksets are supposed to be run.

What's probably happened is you got a crankset that is designed for a shorter BB spindle. Of greater concern than the gap is that your drive side crank with the chainrings is pushed outboard and your chain-line has been messed up.

What you need to do is find the correct spindle length to give you the appropriate  chain-line.