The standard Servo library controls upto 12 servos per 16-bit timer. The Uno has one 16-bit timer, the Mega four 16-bit timers, so 12 and 48 servos respectively (a little short of 52, alas,
it might be possible to tweak the Servo library to support 13 servos per timer to fix that).
Alternatively there are shields that drive multiple servos in various ways I believe.