Raditaz will only use up too much space on your phone depending on the number of tracks you decide to store in your station. You can have as many Raditaz stations as you like. The more stations you have, the more they use up the available space.
In the settings there is a slider you can move to set how much space it uses to cache songs. It does that to use less data to stream the songs. You can just slide it to 0 to not use any space. Think it defaults at 1 gb.