It seems that Adam Paul had another horticulturist son, Evan: See this from the Gardeners' Chronicle of March 6, 1852, p. 145:

"Evan Paul, son of the late Adam Paul, of the Cheshunt Nurseries, and for the last four years with Messrs. J.A. Henderson and Co., of the Pine-apple Nurseries, London, respectfully informs his friends and the public that he is about to open an establishment in the Nursery and Seed line at Derby. It will be his constant aim to obtain every novelty of merit among Trees, Plants, and Seeds of the best quality and purest race, which his long knowledge of the leading members of the profession offers him facilities of doing. He hopes by this course, and a careful attention to business, to obtain the support and confidence of lovers of gardening, which have been so long accorded to his father and brothers at the Cheshunt Nurseries."

His obligations to creditors were being undertaken May 15, 1860, G. Paul being the assignee (Solicitor's Journal & Reporter, vol. 4, 1860, p. 572).

He died May 24, 1871, age 45, at Cheshunt, according to the Gardener's Chronicle, vol. 31, 1871, p. 715.