Except as authorized under Section 3.061 of this Act, no bank holding company other than an Illinois bank holding company, may control any Illinois bank or own more than 5% of the voting shares of any Illinois bank, unless: (a) such bank holding company acquired such control or voting shares under circumstances described in (A), (B), (C), (D) or (E) of subsection (h) of Section 2 of this Act; or (b) such bank holding company qualifies under the provisions of Section 3.071.