FLINT, Mich. — Regardless of the outcome of Republican presidential primaries in Michigan and Arizona on Tuesday, Mitt Romney and Rick Santorum appear headed for a showdown next week in Ohio.

Both candidates plan to dash there later this week. The candidates and their allies already are spending heavily on advertising in the Buckeye State. It’s one of 10 that vote a week from Tuesday, with 419 delegates to the Republican National Convention at stake.

“An awful lot of Ohioans are just tuning in to this,” said Terry Casey, a veteran Republican campaign strategist in that state. “It’s going to be a sprint.”

Beyond Ohio, Romney was looking to contests in the West while Santorum focuses on the South.

Rival Newt Gingrich, seeking to inject momentum into his struggling bid, was working to make his stand in his former home state of Georgia and nearby Southern states that also vote on the mega-contest day of March 6. The former House speaker told reporters Sunday: “We hope to win in Georgia, we hope to do well in Oklahoma and Tennessee. We may surprise people in Idaho. We think we have a real fighting chance in Ohio.”