We present the ATLAS ^ { 3 D } H i survey of a volume-limited , complete sample of 166 nearby early-type galaxies ( ETGs ) brighter than M _ { \mathrm { K } } = -21.5 .
The survey is mostly based on data taken with the Westerbork Synthesis Radio Telescope , which enables us to detect H i down to 5 \times 10 ^ { 6 } - 5 \times 10 ^ { 7 } M _ { \odot } within the survey volume .

We detect H i in \sim 40 percent of all ETGs outside the Virgo galaxy cluster and in \sim 10 percent of all ETGs inside it .
This demonstrates that it is common for non-cluster ETGs to host H i .
The morphology of the detected gas varies in a continuous way from regular , settled H i discs and rings to unsettled gas distributions ( including tidal- or accretion tails ) and systems of gas clouds scattered around the galaxy .
The majority of the detections consist of H i discs or rings ( 1/4 of all ETGs outside Virgo ) so that if H i is detected in an ETG it is most likely distributed on a settled configuration .
These systems come in two main types : small discs ( M ( H i ) < 10 ^ { 8 } M _ { \odot } ) , which are confined within the stellar body and share the same kinematics of the stars ; and large discs/rings ( M ( H i ) up to 5 \times 10 ^ { 9 } M _ { \odot } ) , which extend to tens of kpc from the host galaxy and are in half of the cases kinematically decoupled from the stars .

Neutral hydrogen seems to provide material for star formation in ETGs .
Galaxies containing H i within \sim 1 R _ { \mathrm { e } } exhibit signatures of on-going star formation in \sim 70 percent of the cases , \sim 5 times more frequently than galaxies without central H i .
The ISM in the centre of these galaxies is dominated by molecular gas .
In ETGs with a small gas disc the conversion of H i into H _ { 2 } is as efficient as in spirals .

The ETG H i mass function is characterised by M ^ { * } \sim 2 \times 10 ^ { 9 } M _ { \odot } and by a slope \alpha \sim - 0.7 .
Compared to spirals , ETGs host much less H i as a family .
However , a significant fraction of all ETGs are as H i -rich as spiral galaxies .
The main difference between ETGs and spirals is that the former lack the high-column-density H i typical of the bright stellar disc of the latter .

The ETG H i properties vary with environment density in a more continuous way than suggested by the known Virgo vs. non-Virgo dichotomy .
We find an envelope of decreasing M ( H i ) and M ( H i ) / L _ { \mathrm { K } } with increasing environment density .
The gas-richest galaxies live in the poorest environments ( as found also with CO observations ) , where the detection rate of star-formation signatures is higher .
Galaxies in the centre of Virgo have the lowest H i content , while galaxies at the outskirts of Virgo represent a transition region and can contain significant amounts of H i , indicating that at least a fraction of them has joined the cluster only recently after pre-processing in groups .
Finally , we find an H i morphology-density relation such that at low environment density ( measured on a local scale ) the detected H i is mostly distributed on large , regular discs and rings , while more disturbed H i morphologies dominate environment densities typical of rich groups .
This confirms the importance of processes occurring on a galaxy-group scale for the evolution of ETGs .