Wash the rice until the water rinses clear. Drain the rice in a colander and let it stand for 30 minutes. Place the rice in a pot or rice cooker, and add 4 cups of water or follow the instructions on a rice cooker. Bring the water to a boil. Reduce the heat to a simmer and cover the pot. Cook for 15 minutes. Remove the cover, place a damp towel over the rice, and let cool for 10 minutes.
You can find sushi vinegar prepared at a grocery story or you can easily make it by pouring the vinegar, sugar and salt into a pan under low heat until the sugar and salt are dissolved. If you like sweeter vinegar, just add more sugar.
Pour sushi vinegar over cooked rice and mix it gently. You can do this in a wooden bowl for making sushi rice or in your rice cooker by turning off the cooker and pouring the vinegar and mixing gently and evenly and leaving it until it cools down to room temperature. The lid should remain open.
Cover a makisu (sushi rolling mat) with plastic wrap. Place half of a sheet of the seaweed over the plastic on the mat. Place a handful of rice across the seaweed and spread it evenly over the seaweed. Toss the imitation crab with the mayonnaise in a small bowl. Place some of the imitation crab meat meat along the center of the rice. Add some cucumber and avocado along the center of the rice. Using the mat and plastic wrap, roll the rice around the filling and press lightly to seal. Remove the mat and plastic wrap and sprinkle the roll with sesame seeds. Cut the sushi roll into bite sized pieces. Repeat with the remaining ingredients.