Which theory maintains that new organs arise according to the needs of an organism and that the size of the organs is determined by the size they...

The idea of "use and disuse", that is, new organs arise as per the needs of the organism and unused organs are discarded, was proposed by Jean Baptiste Lamarck, a french naturalist, in 1801. And hence the theory is known as Lamarckian Theory or Lamarckism.This was one of the first theories of evolution of species and was later discarded in favor of Darwin's theory. Lamarck stated that organs will change as per the needs...

The idea of "use and disuse", that is, new organs arise as per the needs of the organism and unused organs are discarded, was proposed by Jean Baptiste Lamarck, a french naturalist, in 1801. And hence the theory is known as Lamarckian Theory or Lamarckism. This was one of the first theories of evolution of species and was later discarded in favor of Darwin's theory. Lamarck stated that organs will change as per the needs of the organisms and those that are not used would shrink. He used the example of giraffes and stated that their necks are longer because they have to reach leaves on tall plants. He also postulated that organisms will become more and more complex over time, as their environment changed. 

There are a number of differences between Lamarckism and Darwin's theory of evolution. 

Hope this helps.