How to refuse to work with graduate students?
Assuming you really do not want to work with them and not even check them out if they are suitable candidates, the response is simply: &quot;I do not currently have available slots for grad students.&quot; Not funding, but &quot;slots&quot;. It means time, nerves, energy, whatever else could come into their mind.
If they have no funding, you say you have no funding for them and you do not accept students without funding.
However, if it is simply a case of you not being sure whether you should take them on, then I recommend preparing a few tasks that are relevant to the work you like to do. These should be pieces of homework that are introductory, but relevant to your field and take about 2-4 weeks of time to cover the entry literature and carry out. If they manage to do it, then you may want to reconsider not taking them. You may have a catch on your hand. Alternatively, you can set conditions of your choice.
Yes, if they want to work with you, you can set the conditions, no apologies. There is a reason for the classic &quot;reluctant sensei&quot; trope. It is a real technique to deal with this.
However, a student that thinks they can bully you is an absolute no-no, no matter how good they are. They are going to be nothing but trouble. So, here the answer is simple. First time: &quot;Unfortunately, I cannot take you on as a student. Thank you for your interest.&quot; Don't give reasons. Second time: &quot;As mentioned in my last mail from ..., I cannot take you on.&quot; Third time: silence. If they continue bugging you, divert their mails to spam or block them. If you cannot or are not allowed to do that, simply archive their mails without opening. Don't open them or you will be tempted to answer them.
You do not need to be outright rude yourself, but if they are, they have deserved the silent treatment. Keep in mind: if you know you will not change your mind, no matter how insistive they are, that will shine through and most of them will desist. If they believe to smell insecurity, they will pounce on it.