Some stores opened early at 8am to cope with the expected demand, with several expressing delight at the number of pre-orders for The Casual Vacancy.
Sealed boxes containing copies of the book were delivered yesterday amid tight security, with bookstores under instructions to keep them under lock and key until this morning.
James Aldridge, of Waterstones, said of the chain's Sauchiehall Street store in Glasgow: "We've had a phenomenal amount of pre-orders for the book and will open at 8am for our customers.
"There's been a lot of anticipation from customers, a lot of questions about the book. There's a lot of goodwill towards her hoping the book is a great success. I think she's very dear to a lot of people's hearts. Considering the next few weeks see new books from people such as Jamie Oliver, Tulisa Contostavlos, Steven Gerrard, Terry Pratchett, Cheryl Cole and Rod Stewart to name a few, the buzz surrounding Rowling's book has been great for what is her first adult fiction book."
In Edinburgh, Oliver Petchey, assistant manager at Waterstones West End in Princes Street, added: "We've had lots of pre-orders. We can't go into exact numbers but we're very, very happy with the amount we've had come through, as people are really keen to get their hands on the book."
Rowling was quoted as saying yesterday she liked the "innate respect for privacy in Edinburgh people". She has often visited the Princes Street store but its staff do not make a fuss over her.
At lunchtime yesterday, in the Edinburgh Bookshop in Bruntsfield Place, owner Vanessa Robertson said she was still waiting for the books to arrive from the distributor and copies might have to be borrowed from Waterstones or Blackwells for today's launch.
"It is slightly frustrating, as it was the publishers who wanted us to open at 8am and have a launch breakfast to make a big fuss of the book," she said.
From her own experience, however, she said she believed people were equivocal about the book. "The die-hard Potter fans, the ones who have grown up with Potter, are very excited about it, and ordered it online the moment it was announced, but a lot of other customers are asking, 'Is it any good?' and I say I don't know, because no-one has read it. They are waiting to read the reviews."
Ms Robertson is also concerned by the £20 retail price of The Casual Vacancy. "A lot of customers are saying it is over-priced. We are doing it at £5 off but I think the price is ridiculous. The economies of scale suggest it doesn't have to be that expensive."
Pre-orders for The Casual Vacancy across the UK reportedly reached one million.
Rowling herself has said of it: "I don't think everyone will like the book. But I'm proud of this book. I like this book. It's what it's meant to be. As an author, you can't say more than that."
The 47-year-old author also said on a BBC documentary last night she had "left the door ajar" for a return to the world of Harry Potter but makes it clear there would be no more books about the teenage wizard.
"Where Harry's story is concerned, I'm done. I just think it would be for the sake of milking it and that's just not in me," she said.
"Having said all of that, I have always left the door ajar because I'm not that cruel. If I had a fabulous idea that came out of that world, because I loved writing it, I would do it."
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