Can a goiter grow back after being removed?

I had one side of my thyroid surgically removed along with the goiter growing on that side. How likely is the other thyroid to develop a goiter now that it is working all by itself? How can I prevent a goiter from recurring?

The most common cause for goitre in the world is iodine deficiency (E01); this condition is commonly called endemic goitre. It is curable by mass food-supplementation with iodine (in the form of iodide or iodate), and today remains a problem only in the least affluent countries which lack economic resources to fortify foods with iodine as part of public health programs.

You must identify how and why you got a Goitre

A "diffuse goitre" is a goitre that has spread through all of the thyroid (and is contrasted with a "simple goitre", "single thyroid nodule" and "multinodular goitre").
"Toxic goitre" refers to goitre with hyperthyroidism. These are derived from inflammation, neoplasm, and some kinds of activating autoimmune disease (Graves' disease).
"Nontoxic goitre" (associated with normal or low thyroid levels) refers to all other types (such as that caused by lithium or certain other autoimmune diseases).

Other causes are:

Hashimoto's thyroiditis
Graves-Basedow disease
Juvenile goitre due to congenital hypothyroidism
Neoplasm of the thyroid
Thyroiditis (acute, chronic)
Side-effects of pharmacological therapy

Iodine is necessary for the synthesis of the thyroid hormones triiodothyronine and thyroxine (T3 and T4). In conditions producing endemic goitre, when iodine is not available, these hormones cannot be made. In response to low thyroid hormones, the pituitary gland releases thyroid stimulating hormone (TSH). Thyroid stimulating hormone acts to increase synthesis of T3 and T4, but in excess it also causes the thyroid gland to grow in size as a type of compensation.

Goitre is more common among women, but this includes the many types of goitre caused by autoimmune problems, and not only those caused by simple lack of iodine.