Put rice into a large deep bowl. Fill with cold water and rub rice together with hands until water turns milky white. Drain cloudy water, being careful not to pour out rice. Repeat three or four times until you can see rice through 3 inches of water; drain once more.

Transfer rice to a saucepan; add kombu and 3 cups water. Let stand 30 minutes. Cover; bring to a boil over high heat. Reduce heat to low; simmer 10 minutes. Remove from heat and let stand, covered, 5 minutes.

Meanwhile, stir together rice vinegar, sugar, and salt in a small bowl until dissolved.

Remove and discard kombu; stir in vinegar mixture until no lumps remain. Spread rice mixture onto a rimmed 9x13 baking sheet. Let cool to room temperature.

Lay one sheet of nori on a sushi mat lined with plastic wrap; spread 1 cup of rice over nori with damp fingers, leaving a 1-inch border along one edge. Arrange desired fillings crosswise just off center of rice. Carefully lift filled edge of nori and roll over filling toward unfilled edge, tucking as you roll. Brush unfilled edge of nori with water; press to seal. Cut each roll into 8 pieces. Repeat with remaining nori, rice, and fillings.