Motor function

Is there a connection between gross motor skills, fine motor skills, and graphomotor skills? Or, in other words, if a child has difficulty writing, does it sometimes make more sense to send him or her outside to play than it does to have him or her practice drawing loops?

We are interested in what influence motor skills - for example sitting posture and pen grip, but also more general motor skills such as steady walking or accurate throwing and catching - have on the acquisition of writing and reading, and more specifically on handwriting, and how large these differences are between children. Which requirements are necessary for children to best learn handwriting, and what is the relationship between handwriting and higher cognitive processing stages (for example segmentation and memory)?