The things affecting operation of a transformer
From experience, I note that the ratio of windings determines the limiting case assuming perfect efficiency.  When dealing with real currents and frequencies, the mass of the core and its magnetic properties add limits.
A small transformer will have a severe voltage drop if you demand a high current.  Usually, the transformer's rated voltage is specified at its rated current.
Different cores (ferrite vs soft iron, etc) are efficient at different frequencies, so iron cores are useful at 50/60hZ while ferrites and specialty materials are used at high frequencies.