Centripetal force is the centre-seeking force & is responsible for circular motion. But what if the centripetal force were acting radially outward? What would happen then?
Centripetal forces are actually just a consequence of the actual forces which act on a body, for instance the centripetal force which a body experiences when it is in orbit arises due to the fact that gravitation is an attractive force! So possibly for the centripetal force to operate in a opposite direction gravitation should be a repulsive force! (For large scale i.e. cosmic, events.). Objects would not orbit around each other but just be deflected from each other, just as it happens when like charges move towards each other. There would be no circular motion since there would be no force to make the objects trajectory circular. I hope I have been clear enough.
It would be called centrifugal force. By definition you call it centripetal when it it is towards the center, and centrifugal if it acts opposite to it. If you have a centripetal force with an object in orbit, and suddenly you make it centrifugal (repulsive), the object will fly off, but I cannot tell if it will be an hyperbolic path without making the actual calculations (plus it also depends on the caracteristics opf the centrifugal force (is it constant, does it decreses or increases as $1/r^2$, etc).