Is there a tool / toolbox in ArcGIS to create quadrats on a population? I have a point feature classes with 1 billion points (divided to 10 almost equal feature classes) that I want to take samples from and I want to use quadrats to describe the data.

There is no optimal size for each quadrat that I want to create, I would rather go with the default value the software suggests.

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In ESRI parlance, systematic quadrats are referred to as a fishnet. You can perform the analysis you are describing by first using the "Arctoolbox > Data Management Tools > Feature Class > Create Fishnet" tool. You will have to define the parameters of the quadrat sizes as there is no sensible default.

Once you have the fishnet polygons created you can use the Arctoolbox > Analysis Tools > Overlay > Intersect" tool to relate the points and fishnet polygons.

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I would use 1 of 2 tools.

1) Grid Index Features (Cartography Tools>Data Driven Pages) This will create a grid that just drops over your chosen feature. It is very handy for an even distribution of grid areas.

2) Create Cartographic Partitions (Cartography Tools>Generalisation) This will create grid squares of varying sizes which cover certain amounts of a certain feature. For example, I used this to create areas that contained equal amounts of point features over a geographical area.

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