A ballanced antenna is one that has equal currents flowing in 'both' of it's halves. The shape of the antenna doesn't make much differnece (if any). That means that a groundplane can also be a ballanced antenna if both halves (vertical element and radial system) have equal currents flowing in them. The number of radials makes no significant difference (as long as there's at least one of them!).
How an antenna is fed can make a difference (direct feed, matching system, etc.). But, if done correctly, no significant difference, if the currents are 'equal' (and opposite, BTW). The imdeance matching system, gamma, beta, whatever kind of match, all have properties that can disturb the 'balance'. The 'trick' is to minimize those 'disturbabces', keep the ballance.
Another point of imballance is how the thing is fed, what kind of feed line. A coaxial feed line is not a ballanced feed line, so, the 'ballance' between the two has to be maintined. There are two basic ways of going about that, change to a ballanced feed line, or provide some kind of 'interface' between the antenna and coax. The most common type of interface is a balun. Another means is by using a 'choke'. A 'choke' works because of the way coax conducts stuff, center conductor and ~insides~ of the braid. The choke keeps/reduces the currents flowing on the ~outside~ of the braid. That's not the easiest idea to understand, but true none the less (the inside of braid conductor and outside of braid conductor thingy). Another way of looking at it is that it doesn't really mater what ~actually~ happens as much as what ~appears~ to happen. The 'biggie' about an unballanced radiator is the 'side affects', not necessarily the actual radiation. Thats from the practical point of view.
That help any?
- 'Doc
PS - After rereading this it looks like this isn't one of my 'good spelling' days. Corrected a couple, and got tired of it. Since there really isn't any 'new' words in this, I'll bet you can figure out which are mispelled.