A Hazelnut isn't so much a tree as a thicket. Left to its own devices, a young Hazelnut will throw up three or four strong central trunks, followed by smaller suckers all around. These suckers will in turn grow on to become trunks, while the plant slowly spreads outwards by sending up more and more suckers. The original trunks in the middle of all this will slowly die off.
There were three Hazlenut trees here when we moved in, and they make a lot of nuts. The main beneficiaries are the local red squirrels, but I did manage to get a bowlful last year. Those nuts that don't get nabbed tend to germinate so I have a steady supply of nut trees that I put around the garden. I'm actually making a "nut tree trail" that I hope will tempt the squirrels to come foraging into the garden from the uncultivated scrub and woods next door.
Looking after Hazelnuts is a question of managing the growth. If you cut off all the suckers every year, you are left with a tidy-ish tree, but it will slowly but surely die. You need to allow a few suckers to remain as the core of a new plant, whilst cutting off the old trunks over time. A good dollop of manure around the base once a year is a good idea too.
The tree in the picture is one of the originals, and has three main parts; the old central branch (just one left, I have cut out the others), three or four strong new branches that are growing vertically upwards, and a thicket of suckers around the base. These suckers I'll leave in place and cut them next Autumn, by which time they should be big enough to make decent plant stakes. The suckers I left 2 and 3 years ago are doing fine, growing into nice vertical trunks that will replace the old one, so I will leave them alone. Then in the Winter, I'll cut another big branch off the old tree, I expect to have replaced the entire tree over the next four years or so.