Say a candidate has met with a potential PhD supervisor and it was rather evident that he would be willing to take on the candidate. You have emailed a lot and met in person a few times, but nothing has been formalised yet.
Suppose now the candidate decides to take it into a different direction simply because there are better options.
What is the most polite way to withdraw ? Is it polite to send an email and explain, or does this come across as arrogant since a PhD candidate is not really in the position to turn down a Professor ? Would it be better simply not to get in touch again ? Is there some standard etiquette in the US and/or the UK ?