For an almost discrete family \(\mathcal A\subset [\kappa]^\lambda\), with \(\kappa\) and \(\lambda\) infinite cardinals such that \(\lambda\le\kappa\), denote by \(\Psi(\mathcal A)\) the corresponding Mrówka space. If \(\lambda=\kappa\) then \(\Psi(\mathcal A)\) has a \(G_\lambda\)-diagonal whereas if \(2^\lambda<\kappa\) and \(\mathcal A\) is maximal then \(\Psi(\mathcal A\setminus\mathcal B)\) does not have a \(G_\lambda\)-diagonal when \(\mathcal B\subset\mathcal A\) and \(|\mathcal B|\le\lambda\). It is also shown that if \(X\) has a regular \(G_\lambda\)-diagonal and a local decreasing base of cardinality \(\chi(X)\) at each \(x\in X\) then \(|X|\le 2^{dc(X)\chi(X)\lambda}\). Corollaries are drawn to show that a first countable space with a regular \(G_\delta\)-diagonal and satisfying the discrete countable chain condition has cardinality at most \(\mathfrak c\).