Maximally embeddable components

We investigate the partial orderings of the form $${\langle \mathbb{P}(\mathbb{X}), \subset \rangle}$$〈P(X),⊂〉 , where $${\mathbb{X} =\langle X, \rho \rangle }$$X=〈X,ρ〉 is a countable binary relational structure and $${\mathbb{P} (\mathbb{X})}$$P(X) the set of the domains of its isomorphic substructures and show that if the components of $${\mathbb{X}}$$X are maximally embeddable and satisfy an additional condition related to connectivity, then the poset $${\langle \mathbb{P} (\mathbb{X}), \subset \rangle }$$〈P(X),⊂〉 is forcing equivalent to a finite power of (P(ω)/ Fin)+, or to the poset (P(ω × ω)/(Fin × Fin))+, or to the product $${(P(\Delta )/\fancyscript{E}\fancyscript{D}_{\rm fin})^+ \times ((P(\omega )/{\rm Fin})^+)^n}$$(P(Δ)/EDfin)+×((P(ω)/Fin)+)n , for some $${n \in \omega}$$n∈ω . In particular we obtain forcing equivalents of the posets of copies of countable equivalence relations, disconnected ultrahomogeneous graphs and some partial orderings.