  Following a characterization [10] of locally tabular logics with finitary (or
unitary) unification by their Kripke models we determine the unification types
of some intermediate logics (extensions of {\sf INT}). There are exactly four
maximal logics with nullary unification ${\mathsf L}(\mathfrak R_{2}+)$,
${\mathsf L}(\mathfrak R_{2})\cap{\mathsf L}(\mathfrak F_{2})$, ${\mathsf
L}(\mathfrak G_{3})$ and ${\mathsf L}(\mathfrak G_{3}+)$ and they are tabular.
There are only two minimal logics with hereditary finitary unification:
${\mathsf L}$($\mathbf F_{un}$), the least logic with hereditary unitary
unification, and ${\mathsf L}$( $\mathbf F_{pr}$) the least logic with
hereditary projective approximation; they are locally tabular. Unitary and
non-projective logics need additional variables for mgu's of some unifiable
formulas, and unitary logics with projective approximation are exactly
projective. None of locally tabular intermediate logics has infinitary
unification. Logics with finitary, but not hereditary finitary, unification are
rare and scattered among the majority of those with nullary unification, see
the example of $\mathsf H_3\mathsf B_2$ and its extensions.
