For uniform circular motion, what happens if the centripetal force is greater than or less than ..?

"what happens if the centripetal force is less than the tension in the string?"

It is ALWAYS less than the tension in the string. Only the horizontal component of the tension (in the horizontal circle situation consider)...causes the centripetal acceleration of the object. The vertical component of the tension opposes the Earth's gravity acting on the object.

"what happens if the centripetal force is greater than the tension in the string?"

In the situation of the horizontal circle...that cannot happen. There isn't any other horizontal force acting on the object OTHER THAN the tension in the string. The net force on the object CANNOT be greater than the tension in the string.

Note: remove the term "centripetal force" from your vocabulary. That is leading you to misconceptions.

THE ONLY forces acting on an object whirled around on a string are the tension in the string and gravity (and air drag if you care).

No additional force is added to the situation just because it is in circular motion...and use of the terms "centripetal force" and "centrifugal force" make you think that is so.

"centripetal force" and "centrifugal force" are the two most unnecessary and confusing terms in introductory physics.

If your object is making a horizontal circle and the tension in the string is T, the centripetal force will be Tx = T cos(theta); where theta is the angle of the string wrt the horizontal. As you can see Tx < T in normal cases since cos(theta) <= 1.00. So nothing out of the ordinary will happen when Tx < T.

When Tx >= T we would have Tx/T = cos(theta) = 1.00 when Tx = T and theta = 0 deg. This means the string is straight out and horizontal; so that when Tx > T, the string will have broken and the suspended object will fly out from its momentum and hit your instructor in the eye. The tension in the classroom will have risen to unparalleled levels. The tension in the string, on the other hand, will have gone to zero.

Centripetal force is what's keeping the body in its circular path. Try this - put a weight on a string and swing it around above your head. Then let go. What happens?