Question
How deep does main root system go down into ground on tree and how far do roots spared out ward.

Answer
Tree root systems are something often misunderstood.  Some think trees have tap roots, others think that the root system goes as deep as the tree is tall.  

Roots perform two primary functions, that of structural support, gathering nutrients and moisture and oxygen.  The oxygen is used in the respiration process, or conversion of sugars into energy.  The sugars are created during the photosynthesis process, and stored until needed, then the roots gather the necessary oxygen to convert into energy.

To meet these needs, tree roots are hard, woody and softer, flexible and non-woody.  

The non-woody roots are in the upper few inches of soil, absorbing the water, nutrients and oxygen needed by the tree.  These are often called feeder roots.
Some trees even have smaller hair like roots extensions on these feeder roots, mostly found in deciduous trees.  

The larger, woody like roots provide the support for the tree. They also transport and store the minerals and water or carbohydrates sent to/through them. These roots generally grow horizontally and in a radial fashion outward from the tree.

The vast majority of the root systems in most trees is in the upper ten to eighteen inches, due to the abundance of oxygen and moisture present. However root systems can vary slightly for each tree species.   The structural roots generally will extend out to the drip line, while feeder roots go outward beyond that to 2-3 times the drip line, and in some cases even beyond that. ( have been known to extend 5-6 times drip line ).

Often you may hear that the majority of feeder roots are concentrated at the dripline of the tree, however in reality roots extend much beyond that  

For depth, roots will grow where they find oxygen, water, minerals and favorable soil conditions, these however are usually found in the top few inches of soil.   This is why you may have seen trees uprooted during heavy winds, when the soil is heavily rain saturated and the whole root plate rotates.  This is often not root failure, but failure of the soil and support area.  

You have shown a Bartlett pear, however regardless of the tree, they all have the same needs and grow in similar fashion given similar conditions.  ( there are some differences between conifers and deciduous trees.

This is why when transplanting a tree such a large root area is recommended to be retained to ensure success in transplant. ( size does vary by diameter/caliper of tree but is detailed in ANSI Z60.1 and if you need I can provide recommendations for tree sizes.

I hope this helps, if you need more please ask.