Hi,
I've also been offered a Quota studentship and my form was sent off a couple of weeks ago. I e-mailed the ESRC a few days ago to ask about timings etc. and they said they will send through the confirmations to the host university early in August.
It'll be so nice to finally get everything sorted in black and white. I was a bit paranoid about the whole procedure but my university has reassured me that the decision to nominate a student is entirely theirs and the ESRC are simply just making sure you fit the basic criteria.