I have a shapefile that contains 10,608,268 polyline features.
What is the maximum limit for records that a shapefile can contains?
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There is a 2 GB size limit for any shapefile component file, which translates to a maximum of roughly 70 million point features. The actual number of line or polygon features you can store in a shapefile depends on the number of vertices in each line or polygon (a vertex is equivalent to a point).
I echo the comment of @Vince:
There are several dynamic buffers involved. I could construct a geometry which was too large to fit in a single [shape], or two that would cause the second to overflow. In your case, 4000 bytes of attributes would prevent creation over 536k features, no matter how many vertices. Note that this isn't a limit of ArcGIS but of the shapefile format itself. My recommendation: Don't use shapefiles. They are archaic, with too many limitations with modern datatypes and volumes.