A patient presented with local gigantism of the leg and increased pulsations of the lower limb veins. Most probable diagnosis is :
Tumor
AV fistula
Varicose veins
Incompetence of the saphenofemoral junction
The patient is having congenital AV fistula which has caused overgrowth of the leg.
Arteriovenous fistula (AVF) 

AVF may be congenital or acquired (by the trauma of a penetrating wound, or surgically created for renal dialysis)
Structural effect on veins → Veins are arterialised*, they become dilated tortuous and thick walled.
Physiological effects of fistula -
Increased pulse pressure (Increased systolic & decreased diastolic)
Enhanced venous return result in Increased HR* and Increased CO*.
Left ventricular enlargement and later cardiac failure may occur
A congenital fistula in the young may cause overgrowth of limb*.
In the leg, indolent ulcers may result* from relative ischemia below the short circuit.

Clinical signs

A pulsatile swelling*
A thrill on palpation*
Continuous bruit on auscultation*
Nicoladonis sign' or Branham sign* → Pressure on the artery proximal to fistula causes the swelling to diminish in size, a thrill or bruit to cease, the pulse rate to fall and the pulse pressure return to normal.