  Some new Hamiltonian systems of quasi-Painlev\'e type are presented and their
Okamoto's space of initial conditions computed. Using the geometric approach
that was introduced originally for the identification problem of Painlev\'e
equations, comparing the irreducible components of the inaccessible divisors
arising in the blow-up process, we find bi-rational, symplectic coordinate
changes between some of these systems that give rise to the same global
symplectic structure. This scheme thus gives a method for identifying
Hamiltonian systems up to bi-rational symplectic maps, which is performed in
this article for systems of quasi-Painlev\'e type having singularities that are
either square-root type algebraic poles or ordinary poles.
