admissions: how to transfert from one university to another?

well, I explain: last year I applied for graduate phd studies to two
universities: the BIGUNIVERSITY, and the MEDIUMUNIVERSITY located
really NEARBY. I did NOT get admitted to the BIGUNIVERSITY, but I was
admitted to the MEDIUMUNIVERSITY; the reason very likely was that I
did not have a governmental award/scholarship that year to back up my
application.

Now this year very likely I am going to be awarded a scholarship
(during the month of march) which can be hold in any university (that
is, you dont have to specify which university you want when you
apply).

My question: what is the best way to get a transfert from
MEDIUMUNIVERSITY to BIGUNIVERSITY?:

either: 1. talk to a professor of BIGUNIVERSITY when I get the award,
and say that I like his research(actually, I know in some very precise
details what is his research, because I have taken one of his graduate
courses and I have also taken other graduate courses of BIGUNIVERSITY
(because it is a nearby university) ) and that I would prefer to
continue as his student? Then if that professor accept he may help me
to get in throught special procedures (transfer student, late
application, etc..)

or: 2. apply for admission throught normal procedures? But then I dont
know where I will get the Letters of recommandation which are
required.. (I am not going to ask the professors of my current
MEDIUMUNIVERSITY for such letters huh ???)

well, does anyone knows how all this world works? (I think such things
should be possible..)