User blog comment:Primussupremus/Where would the Busy Beaver function come in the fast growing hiearchy./@comment-1605058-20170416100356

BB function would land above \(f_\alpha(n)\) for any ordinal \(\alpha<\omega_1^\text{CK}\) if you choose fundamental sequences in a recursive way. Whether \(f_{\omega_1^\text{CK}}\) depends on fundamental sequences chosen.

I am not aware of any books about ITTMs, but the original paper which has introduced them contains quite a bit of relevant information. I'm afraid it will be difficult to find any less technical sources if you are looking for such.