Eleven candidate damped Ly \alpha absorption systems were identified in twenty-seven spectra of the quasars from the APM z _ { > } \atop { { } ^ { \sim } } 4 survey covering the redshift range 2.8 \leq z _ { absorption } \leq 4.4 ( 8 with z _ { absorption } > 3.5 ) .
High resolution echelle spectra ( 0.8Å FWHM ) have been obtained for three quasars , including two of the highest redshift objects in the survey .
Two damped systems have confirmed HI column densities of N _ { HI } \geq 10 ^ { 20.3 } atoms cm ^ { -2 } , with a third falling just below this threshold .
We have discovered the highest redshift damped Ly \alpha absorber known at z = 4.383 in QSO BR1202 - 0725 .

The APM QSOs provide a substantial increase in the redshift path available for damped surveys for z > 3 .
We combine this high redshift sample with other quasar samples covering the redshift range 0.008 < z < 4.7 to study the redshift evolution and the column density distribution function for absorbers with log N _ { HI } \geq 17.2 .
In the HI column density distribution f ( N ) = kN ^ { - \beta } we find evidence for breaks in the power law , flattening for 17.2 \leq \log N _ { HI } _ { < } \atop { { } ^ { \sim } } 21 and steepening for \log N _ { HI } > 21.2 .
The breaks are more pronounced at higher redshift .
The column density distribution function for the data with log N _ { HI } \geq 20.3 is better fit with the form f ( N ) = ( f _ { * } / N _ { * } ) ( N / N _ { * } ) ^ { - \beta } exp ( - N / N _ { * } ) with log N _ { * } = 21.63 \pm 0.35 , \beta = 1.48 \pm 0.30 , and f _ { * } = 1.77 \times 10 ^ { -2 } .
We have studied the evolution of the number density per unit redshift of the damped systems by fitting the sample with the customary power law N ( z ) = N _ { 0 } ( 1 + z ) ^ { \gamma } .
For a population with no intrinsic evolution in the product of the absorption cross-section and comoving spatial number density this will give \gamma = 1 / 2 ( \Omega = 1 ) or \gamma = 1 ( \Omega = 0 ) .
The best maximum likelihood fit for a single power law is \gamma = 1.3 \pm 0.5 and N _ { 0 } = .04 ^ { + .03 } _ { - .02 } , consistent with no intrinsic evolution even though the value of \gamma is also consistent with that found for the Lyman limit systems where evolution is detected at a significant level .
However , redshift evolution is evident in the higher column density systems with an apparent decline in N ( z ) for z > 3.5 .