<p>Suppose for a moment that you got an informal offer that a supervisor will take you if you’re admitted. Should I mention that when I write e-mails to other professors doing similar research to the one I got the offer from?</p>
<p>No. Definitely not.</p>
<p>The time to compare/discuss the merits of comparative offers is <em>after</em> you have admission/funding letters in hand.</p>