Rasterize create smaller rasters where the no daata values are excluded from the raster. To do this include the -a_nodata value=0 function in the command line of the rasterrize tool, where 0 is the nodata value. The process is as follows:
Trying the -at function. Rasterize based on first value encountered in processing... Top left, bottom right? Seems random...

But does not do a better job than simply using the defaults and taking the centre point...

Except in the case of lone-standing, small featues where the centrepoint would be easily missed as in the following case

Versus this case, where the - at function is used and no feature is missed in the rasterization process

