I've always thought of underwriters of public offerings like realtors. They get a set fee structure negotiated pre the offering, to handle selling the product. I may be wrong. I haven't much experience in that area. Just pay attention to when share structure changes. Don't care how. I think price is determined threw advise of underwriter and wants/needs of the company. And the offering can stay in place till the company sells all or gives up. For all I know there may be a time limit contract restriction between company & underwriter. Just like selling real-estate. LOL
Check with BigBake1 he has a handle on FINRA filings info.