Handling PhD funding offers that come before hearing back from all schools I applied to So I applied to several PhD programs at different schools of probably different levels of selectivity and prestige. From a few of these schools I have been admitted and in contact with certain professors there who are suggesting that I will receive full funding to go there. In one case, this funding will be in the form of a fellowship from the school. The only hang up is that they would like me to make a decision on these offers quickly. In one case, I think they want to figure out if I would accept the fellowship if offered to me so they can extend it to someone else if I wouldn’t accept. 

The problem is, the two schools I am most interested in have not yet admitted me and no professors from those schools have reached out to me. I would like to know what the result of my application to these schools will be before deciding. Should I just tell the other schools to wait? I worry that I may not receive a fellowship offer from one of these schools for delaying my decision too long (and would maybe be funded through some other means). Another option I see would be to reach out to the universities that have not admitted me yet and try to initiate conversations about working in professors groups and gauge how they perceive the strength of my application. 

To summarize my question:
What is the best course of action when a grad school (or specific professor you want to work with there) pressures you to make a decision on their offer before all other schools you applied to admitted or rejected you? 

I am located in the US, sorry forgot to mention it
This answer applies if your schools of choice are in the United States:

Most major universities in the US are signatories to the "April 15th resolution," which gives students until April 15th to accept offers of admission/financial aid. A full list is here: http://cgsnet.org/ckfinder/userfiles/files/CGSResolution_RevisedOct2017.pdf


  Students are under no obligation to respond to offers of financial support prior to April 15; earlier deadlines for acceptance of
  such offers violate the intent of this Resolution




If the schools you are applying to are in the US and signatories to this resolution, they are not allowed to offer and then withdraw admission/financial aid prior to April 15th. Before that deadline, you can politely inform them that you are waiting for all your offers before making a decision. They might want to pressure you to commit earlier, but you are not compelled to do so.

You are correct, though, in assuming that they would like to offer the fellowship to someone else, if possible. Therefore, the polite thing to do is to inform any school that is no longer in contention as soon as possible, that is, as soon as you have another offer you plan to accept, and no sooner.

You could reach out to the schools you are waiting to hear from, but I wouldn't pester them, it is still fairly early in the acceptance calendar (again, from a US perspective) and admissions committees are still meeting to make decisions.