To prepare rice for this or any other sushi dish, rice must be pickled. Combine vinegar and sugar in an enamel saucepan and bring to a boil.
Cook, stirring until sugar is completely dissolved. Remove from heat. Stir 2 tablespoons of vinegar, sugar mixture into the cooked, still warm rice. Warm rice absorbs the mixture more completely.
Stir sesame seeds into rice. Press pickled rice into a square in a small serving platter. Cut rice into square and leave rice squares in place.
Press each square lightly so that rice clings and place in a small dab of wasabi paste each. Press a bit of crabmeat, fish roe and avocado on each square.
