That depends on the kind of float, you can float in three different ways: emit new stock, sell existing stock, a combination of those two. Any new stock emitted will have the bulk of the funds (minus fees and all that) deposited in the company, selling existing stock will have the bulk of the funds deposited with the existing share holders.

It isn't rare for there to be a lock-up period before existing stock holders are able to sell their shares on the market to avoid people dumping stock they know is worth less than the float price. This is because there is a fair chance that those closely involved with the company have a better long term view on what the company will do than the market so it takes a while to get any post float surprises to be priced in. That's one reason why IPOs tend to be tricky to price: overprice and the stock will drop after the float and those that bought the IPO will feel burned, underprice and you're leaving money on the table.