1. In a medium saucepan, cover potatoes with cold water by 1 inch. Bring to a boil, and add salt. Reduce heat to a simmer, and cook until the potatoes are just tender when pierced with a fork, about 15 minutes. Drain in a colander, and let the potatoes cool completely. Slice into 1-inch pieces; set aside.

2. In a small saute pan, heat 2 tablespoons oil over medium-high heat until hot but not smoking. Add capers; cook, stirring occasionally, until crisp, about 3 minutes. Using a slotted spoon, transfer to a paper-towel-lined plate.

3. Heat grill to medium. Cut squid bodies open to make flat pieces. Holding a sharp knife at a 30-degree angle, score the inner side of each squid in a crosshatch pattern, being careful not to cut all the way through. Toss the squid bodies and tentacles with 2 tablespoons oil; season with salt and pepper. Grill squid, turning once, until just cooked through and nicely charred (squid will curl up as it cooks), 2 to 3 minutes. Be careful not to overcook because squid will toughen. Cut into 2-inch pieces.

4. In a small bowl, whisk together lemon juice and remaining 6 tablespoons oil. In a medium bowl, combine reserved potatoes, fennel, and parsley. Coat with half the lemon mixture, and season with salt and pepper. In another bowl, toss squid with remaining lemon mixture; season with salt and pepper.

5. To serve, place about 2 tablespoons skordalia sauce on each plate. Top with a mound of potato salad. Place squid on top, and garnish with the capers.