What is the impact of different modes on pseudo randomness of AES? AES in CBC-MAC mode is proven to be good PRF . But is there any study done on other modes ? how good is ECB mode as PRF ?
Yes, of course other modes have been studied.

See this paper for one study, and that paper for another study.

The bottom line is that CFB, OFB and CTR modes are also good PRFs (assuming you use random IVs).

As for ECB mode, it is a good PRF if you limit it to inputs of precisely one block (128 bits for AES); it is not a good PRF if you are allowed to submit larger inputs.