For the mashed potato, cut the potatoes into even-sized chunks, not too small. If they are large, quarter them and if they are small, halve them.
Put the potato chunks in a large saucepan of boiling water, and simmer gently until they are absolutely tender - they should take about 25 minutes.
When the potatoes are cooked, drain them and place back in the empty pan. Add the mayonnaise to the potatoes at this point and using a wooden spoon (not a masher or whisk) vigorously mash them. The finished mash should not be completely smooth, but a combination of creamy and chunky mash.
For the tuna steaks, rub olive oil in to both sides then season with salt and freshly ground black pepper. Heat a pan and chargrill for two minutes on each side.