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The \textit{nowhere dense ideal} $\mathcal{NC}$ is introduced. It is acoanalytic ideal of $\omega\times\omega$ whose defining characteristic is thatthe sets of the form $X\times Y$, where $X,Y$ are infinite subsets of $\omega$,are dense in the quotient $\mathcal{P}(\omega\times\omega)\slash\mathcal{NC}$.This quotient has countable partitions and consistently has partitions of size$\omega_1$ while $\mathfrak{a}>\omega_1$. This represents a huge contrast withother definable quotients. Other combinatorial features of this ideal arepresented, as well as some results on a family of similar, higher dimensionalideals.

Small infinite partitions and other features of the Nowhere Centered ideal