I was rejected from UCSD, but I received several very welcoming emails like this from professors at another program. It makes you feel like they are excited about the prospect of you joining them! In my case, the program is the lower ranked of two that I'm deciding between. I haven't experienced that at the higher ranked program, which is one of the reasons I'm still considering both of them. I want to be in a program with professors who are enthusiastic about me working with them.