A true breeding white flowering plant will always produce offspring with white flowers. This is because it carries two identical alleles (versions of the gene) for the white flower trait, which we can represent as "ww".

When this plant self-pollinates or crosses with another true breeding white flowering plant, the offspring will inherit one "w" allele from each parent, resulting in a "ww" genotype. This genotype always results in white flowers.

In summary:

* True breeding white flowering plant genotype: ww

* Offspring genotype: ww

* Offspring phenotype (appearance): White flowers