Boyce is president of Friends of Greenwich Street, the group that cares for the trees and plantings between North Moore and Duane Streets. He wants to see more trees springing from sidewalks around the neighborhood, and the ones that are here, he said, need to be cared for.

Friends of Greenwich Street has applied to the state’s Department of Environmental Conservation for an $8,000 matching grant to help do just that.

With those funds, Boyce hopes to set up an office and hire an intern to help oversee the care of Tribeca’s trees. He plans an adopt-a-tree program that would pair trees with local residents and workers who, with some basic instruction, could give their tree (or trees) some modest maintenance, such as removing root-killing salt at winter’s end.

Boyce, a vice president at the Bank of New York, is ready to hear from volunteers. (E-mail him at president@ greenwichstreet.org.) And if his organization receives the hoped-for grant, it will also launch a block-by-block recruitment effort for its “Tribeca Tree Corps.”

The group also hopes to identify places to plant new trees. The purpose, Boyce said, is to make the neighborhood cooler and to reduce pollution.

Finding such places could be a challenge, with all the sidewalk vaults and other underground encumbrances. But if anyone is up to the task of growing that “urban forest,” as he calls it, it is Steve Boyce.

“I could name 50 spots where there could be a tree,” he said.