Applied to 7. None with the one really good sup i wanted to work with as she wasnt taking newbies ths yr. 2 in the UK, for which I needed detailed proposal. 5 in US which just needed an SOP and an idea of fit with the dpet (Cos in US u dnt start all this til after coursework)...
but ultimately was offered supervision by that one really good sup, without submitting a proposal!!
So, LOL, it differes...in my case I never ask myself this question "u stupid idiot why did u waste all that time and energy applying to 7 places when u could have approached the one you wanted to work with staright away instead of staying happy with the decision that she wasnt taking new people anymore!" but asking myself that makes me feel really stupid, so i dont..