They all spread out, but generally speaking the directivity of an antenna or emitter (assuming optimal design) is proportional to its volume, in wavelengths cubed. So a tiny high-frequency antenna with a volume of five wavelengths cubed has the same directivity as a huge low-frequency antenna also with a volume of five wavelengths cubed. Of course, other things also affect directivity, like temperature, the particular antenna design, etc. That's why I said "generally speaking".
