**Core Concept**
The question is testing the understanding of the pathophysiology of nephrotic syndrome, specifically the changes that occur in the glomerular basement membrane (GBM) and the podocytes in this condition.

**Why the Correct Answer is Right**
The correct answer is A, fusion of foot processes of the glomerular epithelial cells. This is characteristic of minimal change disease (MCD), a common cause of nephrotic syndrome in children. In MCD, the glomerular basement membrane appears normal on light microscopy but shows podocyte foot process effacement on electron microscopy. This is due to the loss of the slit diaphragm, which normally separates the foot processes of adjacent podocytes. As a result, the foot processes fuse, leading to massive proteinuria and hypoalbuminemia.

**Why Each Wrong Option is Incorrect**
**Option B:** Rarefaction of the glomerular basement membrane is not a characteristic feature of nephrotic syndrome. Rarefaction refers to a thinning or decrease in the density of the GBM, which is not typically seen in MCD.

**Option C:** Deposition of electron-dense material in the basement membrane is more characteristic of membranous nephropathy, another cause of nephrotic syndrome. This condition is associated with the deposition of immune complexes in the GBM, leading to thickening and electron-dense deposits.

**Option D:** Thin basement membrane is characteristic of thin basement membrane disease (TBMD), a condition that typically presents with hematuria rather than nephrotic syndrome. TBMD is caused by mutations in the COL4A3 and COL4A4 genes, which code for collagen types IV, components of the GBM.

**Clinical Pearl / High-Yield Fact**
Minimal change disease is the most common cause of nephrotic syndrome in children and is often associated with a good response to corticosteroid therapy. However, relapses are common, and long-term maintenance therapy may be required to prevent recurrence.

**✓ Correct Answer: A. Fusion of foot processes of the glomerular epithelial cells**