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I asked this question as a small question under an answer of another question (How bed leveling is achieved without table screws?), but have been asked to post this as a separate question to answer it with more detail conform SE policy.

One question with respect to automatic bed leveling (also known as ABL): If the bed is tilted and the auto leveling measured this and then the printer adjust the z axis over the position on the bed, will a x-y-point on the first layer be located exactly under the (in model) same x-y-point in a higher layer, or will it be shifted to? I mean, if the bed is 1 mm lower on one side over 10 cm then a top corner of a 10-cm-cube should be also 1 mm shifted, so that the cube still is real cubic and not sheared.

Using automatic bed leveling assists you in getting the print to stick better to the build platform as a result of the print head following the un-uniform geometry or tilt of the build plate.

In, e.g. Marlin Firmware, the bed level correction is fading out over a predefined distance, this is determined by the constant #define ENABLE_LEVELING_FADE_HEIGHT in the printer firmware Configuration.h file and the height can be set with M420 Z<height> (see here).

M420 S1 ; Enable compensation using current grid/mesh
M420 Z10 ; Gradually reduce compensation until Z=10

Yes, a cube will not be perfectly cubic, that is why even with auto bed leveling you need to provide a bed as level as possible, it only should correct for very small deviations.

When the print is smaller than the fade out height, you would indeed get a sheared print, if larger, then the top of the print would be level with respect to the reference plane (this is the level of the x-y plane, basically the level of the hot end carriage). Note that that still can be skew if the printer is improperly calibrated (e.g. when using 2 Z steppers or misalignment of the height on either side).