For the past decade, ionized outflows of a few 100 km/s from nearby Seyfert galaxies have been studied in great detail using high resolution X-ray absorption spectra. A recurring feature of these outflows is their broad ionization distribution including essentially ions (e.g., of Fe) from neutral to fully ionized. The absorption measure distribution (AMD) is defined as the distribution of column density with ionization parameter |d N_H/d (log xi)|. AMDs of Seyfert outflows can span up to five orders of magnitude in xi. We present the AMD of five outflows and show that they are all rather flat, perhaps slightly rising towards high ionization. More quantitatively, a power-law fit for log AMD ~ (log xi)^a yields slopes of 0 < a < 0.4. These slopes tightly constrain the density profiles of the wind, which until now could be addressed only by theory. If the wind is distributed on large scales, the measured slopes imply a generic density radial profile of n ~ r^{-alpha} with 1 < alpha < 1.3. This scaling rules out a mass conserving radial flow of n ~ r^{-2}, or a constant density absorber, but is consistent with a non-spherical MHD outflow model in which n ~ r^{-1} along any given line of sight. On the other hand, if ionization variations are a result of local (delta r) density gradients, e.g. as in the turbulent interstellar medium (ISM), the AMD slopes imply density scaling of n ~ delta r^{-alpha} with 0.7 < alpha < 1.0, which is quite different from the scaling of approximately n ~ delta r^{0.4} found in the Milky Way ISM and typical of incompressible turbulence.
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